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diff --git a/docs/disc08/index.html b/docs/disc08/index.html
index f66d256..ae8023e 100644
--- a/docs/disc08/index.html
+++ b/docs/disc08/index.html
@@ -6,6 +6,9 @@
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
   <title>Discussion 8: The Central Limit Theorem and Hypothesis Testing</title>
   <style>
+    /* Default styles provided by pandoc.
+    ** See https://pandoc.org/MANUAL.html#variables-for-html for config info.
+    */
     code{white-space: pre-wrap;}
     span.smallcaps{font-variant: small-caps;}
     div.columns{display: flex; gap: min(4vw, 1.5em);}
diff --git a/docs/disc09/index.html b/docs/disc09/index.html
index 49316ea..c5f79a7 100644
--- a/docs/disc09/index.html
+++ b/docs/disc09/index.html
@@ -6,6 +6,9 @@
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
   <title>Discussion 9: Total Variation Distance and Permutation Testing</title>
   <style>
+    /* Default styles provided by pandoc.
+    ** See https://pandoc.org/MANUAL.html#variables-for-html for config info.
+    */
     code{white-space: pre-wrap;}
     span.smallcaps{font-variant: small-caps;}
     div.columns{display: flex; gap: min(4vw, 1.5em);}
diff --git a/docs/disc10/index.html b/docs/disc10/index.html
index cd87e26..b38504f 100644
--- a/docs/disc10/index.html
+++ b/docs/disc10/index.html
@@ -6,6 +6,9 @@
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
   <title>Discussion 10: Regression</title>
   <style>
+    /* Default styles provided by pandoc.
+    ** See https://pandoc.org/MANUAL.html#variables-for-html for config info.
+    */
     code{white-space: pre-wrap;}
     span.smallcaps{font-variant: small-caps;}
     div.columns{display: flex; gap: min(4vw, 1.5em);}
diff --git a/docs/fa25-midterm/index.html b/docs/fa25-midterm/index.html
index 296aca1..4f0bce2 100644
--- a/docs/fa25-midterm/index.html
+++ b/docs/fa25-midterm/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/fa25-quiz1/index.html b/docs/fa25-quiz1/index.html
index ae3f7cd..034b0ab 100644
--- a/docs/fa25-quiz1/index.html
+++ b/docs/fa25-quiz1/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
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   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
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index 3dabb62..8bb6a91 100644
--- a/docs/fa25-quiz2/index.html
+++ b/docs/fa25-quiz2/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/fa25-quiz3/index.html b/docs/fa25-quiz3/index.html
index 325519e..099998d 100644
--- a/docs/fa25-quiz3/index.html
+++ b/docs/fa25-quiz3/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/fa25-quiz4/index.html b/docs/fa25-quiz4/index.html
index 56b722b..5c641a3 100644
--- a/docs/fa25-quiz4/index.html
+++ b/docs/fa25-quiz4/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/index.html b/docs/index.html
index 41772a7..34aee52 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -6,6 +6,9 @@
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
   <title>Home – DSC 10 Practice</title>
   <style>
+    /* Default styles provided by pandoc.
+    ** See https://pandoc.org/MANUAL.html#variables-for-html for config info.
+    */
     code{white-space: pre-wrap;}
     span.smallcaps{font-variant: small-caps;}
     div.columns{display: flex; gap: min(4vw, 1.5em);}
diff --git a/docs/lectures/lec10/index.html b/docs/lectures/lec10/index.html
index cfd1103..5bec5b2 100644
--- a/docs/lectures/lec10/index.html
+++ b/docs/lectures/lec10/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
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   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/lectures/lec11/index.html b/docs/lectures/lec11/index.html
index 3724a37..89bb14c 100644
--- a/docs/lectures/lec11/index.html
+++ b/docs/lectures/lec11/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
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   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -3310,8 +3310,7 @@ <h5>Difficulty:
 <p><br></p>
 <hr />
 <h2 id="problem-22">Problem 22</h2>
-<p>Suppose you have a DataFrame called <code>plum</code> with 31
-rows.</p>
+<p>Recall, <code>plum</code> has 31 rows.</p>
 <p>Consider the function <code>df_choice</code>, defined below.</p>
 <div class="sourceCode" id="cb5"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> df_choice(df):</span>
 <span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> df[np.random.choice([<span class="va">True</span>, <span class="va">False</span>], df.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)]</span></code></pre></div>
@@ -3388,6 +3387,11 @@ <h1 class="title"> </h1>
 missing}) \cdot P(\text{row 1 missing}) \cdot ... \cdot P(\text{row 30
 missing}) \\ &amp;= \frac{1}{2} \cdot \frac{1}{2} \cdot ... \cdot
 \frac{1}{2} \\ &amp;= \boxed{\frac{1}{2^{31}}} \end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 83%.</p>
 </div>
 </div>
 </div>
@@ -3439,6 +3443,11 @@ <h1 class="title"> </h1>
 is missing}) \\ &amp;= \frac{1}{2^{31}} + \frac{1}{2^{31}} + ... +
 \frac{1}{2^{31}} \\ &amp;=
 \boxed{\frac{31}{2^{31}}}  \end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 48%.</p>
 </div>
 </div>
 </div>
@@ -3485,6 +3494,11 @@ <h1 class="title"> </h1>
 just row 0 is <span class="math inline">\frac{1}{2^{31}}</span>, and
 this is the same as the answer to the first subpart (<span class="math inline">\frac{1}{2^{31}}</span>); in both situations, we are
 calculating the probability of one specific subset.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 63%.</p>
 </div>
 </div>
 </div>
@@ -3555,6 +3569,11 @@ <h1 class="title"> </h1>
 \frac{1 + 31 + 31 + 1}{2^{31}} \\ &amp;= \frac{64}{2^{31}} \\ &amp;=
 \frac{2^6}{2^{31}} \\ &amp;= \frac{1}{2^{31 - 6}} \\ &amp;=
 \boxed{\frac{1}{2^{25}}} \end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 35%.</p>
 </div>
 </div>
 </div>
@@ -3562,7 +3581,8 @@ <h1 class="title"> </h1>
 <p><br></p>
 <hr />
 <h2 id="problem-23">Problem 23</h2>
-<p>Recall, <code>plum</code> has 31 rows.</p>
+<p>Suppose you have a DataFrame called <code>plum</code> with 31
+rows.</p>
 <p>Consider the function <code>df_choice</code>, defined below.</p>
 <div class="sourceCode" id="cb6"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> df_choice(df):</span>
 <span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> df[np.random.choice([<span class="va">True</span>, <span class="va">False</span>], df.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)]</span></code></pre></div>
@@ -3639,11 +3659,6 @@ <h1 class="title"> </h1>
 missing}) \cdot P(\text{row 1 missing}) \cdot ... \cdot P(\text{row 30
 missing}) \\ &amp;= \frac{1}{2} \cdot \frac{1}{2} \cdot ... \cdot
 \frac{1}{2} \\ &amp;= \boxed{\frac{1}{2^{31}}} \end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 83%.</p>
 </div>
 </div>
 </div>
@@ -3695,11 +3710,6 @@ <h1 class="title"> </h1>
 is missing}) \\ &amp;= \frac{1}{2^{31}} + \frac{1}{2^{31}} + ... +
 \frac{1}{2^{31}} \\ &amp;=
 \boxed{\frac{31}{2^{31}}}  \end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 48%.</p>
 </div>
 </div>
 </div>
@@ -3746,11 +3756,6 @@ <h1 class="title"> </h1>
 just row 0 is <span class="math inline">\frac{1}{2^{31}}</span>, and
 this is the same as the answer to the first subpart (<span class="math inline">\frac{1}{2^{31}}</span>); in both situations, we are
 calculating the probability of one specific subset.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 63%.</p>
 </div>
 </div>
 </div>
@@ -3821,11 +3826,6 @@ <h1 class="title"> </h1>
 \frac{1 + 31 + 31 + 1}{2^{31}} \\ &amp;= \frac{64}{2^{31}} \\ &amp;=
 \frac{2^6}{2^{31}} \\ &amp;= \frac{1}{2^{31 - 6}} \\ &amp;=
 \boxed{\frac{1}{2^{25}}} \end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 35%.</p>
 </div>
 </div>
 </div>
diff --git a/docs/lectures/lec12/index.html b/docs/lectures/lec12/index.html
index 1555472..093ba6a 100644
--- a/docs/lectures/lec12/index.html
+++ b/docs/lectures/lec12/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/lectures/lec13/index.html b/docs/lectures/lec13/index.html
index b40a9e9..f5a1032 100644
--- a/docs/lectures/lec13/index.html
+++ b/docs/lectures/lec13/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -813,81 +813,6 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-7">Problem 7</h2>
-<p>Describe in your own words the difference between a probability
-distribution and an empirical distribution. Give an example of what each
-distribution might look like for a certain experiment. Choose an
-experiment that we have not already seen in this class.</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading7">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse7" aria-expanded="true" aria-controls="collapse7">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse7" class="accordion-collapse collapse"
-aria-labelledby="heading7" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> There are many possible correct answers.
-Below are some student responses that earned full credit, lightly edited
-for clarity.</p>
-<hr/>
-<p><i>Probability distributions are theoretical distributions
-distributed over all possible values of an experiment. Meanwhile,
-empirical distributions are distributions of the real observed data. An
-example of this would be choosing a certain suit from a deck of cards.
-The probability distribution would be uniform, with a 1/4 chance of
-choosing each suit. Meanwhile, the empirical distribution of choosing
-suits from a deck of cards in 50 pulls manually and graphing the
-observed data would show us different chances. </i></p>
-<hr/>
-<p><i>A probability distribution is the distribution describing the
-theoretical probability of each potential value occurring in an
-experiment, while the empirical distribution describes the proportion of
-each of the values in the experiment after running it, including all
-observed values. In other words, the probability distribution is what we
-expect to happen, and the empirical distribution is what actually
-happens.</i></p>
-<p><i>For example: My friends and I often go to a food court to eat, and
-we randomly pick a restaurant every time. There is 1 McDonald’s, 1
-Subway, and 2 Panda Express restaurants in the food court.</i></p>
-<p><i>The probability distribution is as follows:</i></p>
-<ul>
-<li>P(McDonald’s) = 0.25</li>
-<li>P(Subway) = 0.25</li>
-<li>P(Panda Express) = 0.5</li>
-</ul>
-<p><i>After going to the food court 100 times, we look at the empirical
-distribution to see which restaurants we eat at most often. it is as
-follows:</i></p>
-<ul>
-<li>(McDonald’s) = 0.21</li>
-<li>(Subway) = 0.22</li>
-<li>(Panda Express) = 0.57</li>
-</ul>
-<hr/>
-<p><i>Probability distribution is a theoretical representation of
-certain outcomes in an event whereas an empirical distribution is the
-observational representation of the same outcomes in an event produced
-from an experiment.</i></p>
-<p><i>An example would be if I had 10 pairs of shoes in my closet: The
-probability distribution would suggest that each pair of shoes has an
-equal chance of getting picked on any given day. On the other hand, an
-empirical distribution would be drawn by recording which pair got picked
-on a given day in N trials. </i></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 82%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-8">Problem 8</h2>
 <div class="sourceCode" id="cb15"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>results <span class="op">=</span> np.array([])</span>
 <span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(<span class="dv">10</span>):</span>
@@ -906,13 +831,13 @@ <h2 id="problem-8">Problem 8</h2>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading8">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8" aria-expanded="true" aria-controls="collapse8">
+<h2 class="accordion-header" id="heading7">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse7" aria-expanded="true" aria-controls="collapse7">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse8" class="accordion-collapse collapse"
-aria-labelledby="heading8" data-bs-parent="#accordionExample">
+<div id="collapse7" class="accordion-collapse collapse"
+aria-labelledby="heading7" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -963,6 +888,81 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <hr />
+<h2 id="problem-8">Problem 8</h2>
+<p>Describe in your own words the difference between a probability
+distribution and an empirical distribution. Give an example of what each
+distribution might look like for a certain experiment. Choose an
+experiment that we have not already seen in this class.</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading8">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8" aria-expanded="true" aria-controls="collapse8">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse8" class="accordion-collapse collapse"
+aria-labelledby="heading8" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> There are many possible correct answers.
+Below are some student responses that earned full credit, lightly edited
+for clarity.</p>
+<hr/>
+<p><i>Probability distributions are theoretical distributions
+distributed over all possible values of an experiment. Meanwhile,
+empirical distributions are distributions of the real observed data. An
+example of this would be choosing a certain suit from a deck of cards.
+The probability distribution would be uniform, with a 1/4 chance of
+choosing each suit. Meanwhile, the empirical distribution of choosing
+suits from a deck of cards in 50 pulls manually and graphing the
+observed data would show us different chances. </i></p>
+<hr/>
+<p><i>A probability distribution is the distribution describing the
+theoretical probability of each potential value occurring in an
+experiment, while the empirical distribution describes the proportion of
+each of the values in the experiment after running it, including all
+observed values. In other words, the probability distribution is what we
+expect to happen, and the empirical distribution is what actually
+happens.</i></p>
+<p><i>For example: My friends and I often go to a food court to eat, and
+we randomly pick a restaurant every time. There is 1 McDonald’s, 1
+Subway, and 2 Panda Express restaurants in the food court.</i></p>
+<p><i>The probability distribution is as follows:</i></p>
+<ul>
+<li>P(McDonald’s) = 0.25</li>
+<li>P(Subway) = 0.25</li>
+<li>P(Panda Express) = 0.5</li>
+</ul>
+<p><i>After going to the food court 100 times, we look at the empirical
+distribution to see which restaurants we eat at most often. it is as
+follows:</i></p>
+<ul>
+<li>(McDonald’s) = 0.21</li>
+<li>(Subway) = 0.22</li>
+<li>(Panda Express) = 0.57</li>
+</ul>
+<hr/>
+<p><i>Probability distribution is a theoretical representation of
+certain outcomes in an event whereas an empirical distribution is the
+observational representation of the same outcomes in an event produced
+from an experiment.</i></p>
+<p><i>An example would be if I had 10 pairs of shoes in my closet: The
+probability distribution would suggest that each pair of shoes has an
+equal chance of getting picked on any given day. On the other hand, an
+empirical distribution would be drawn by recording which pair got picked
+on a given day in N trials. </i></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 82%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <h2 id="problem-9">Problem 9</h2>
 <p>Suppose we take a uniform random sample with replacement from a
 population, and use the sample mean as an estimate for the population
diff --git a/docs/lectures/lec14/index.html b/docs/lectures/lec14/index.html
index 3958361..93d6a48 100644
--- a/docs/lectures/lec14/index.html
+++ b/docs/lectures/lec14/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/lectures/lec15/index.html b/docs/lectures/lec15/index.html
index ecb6fcc..15e3af8 100644
--- a/docs/lectures/lec15/index.html
+++ b/docs/lectures/lec15/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -650,12 +650,21 @@ <h2 class="accordion-header" id="heading3_5">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer</strong>: Our new sample should have four times as
-many people overall. It doesn’t matter how many of them are from
-District 12.</p>
-<p>The width of our confidence interval is determined by the standard
-error which decreases at the factor of <span class="math inline">\frac{1}{\sqrt(n)}</span> to half the width, we need
-the denominator to increase by a factor of 2. Therefore, we need 4x more
-data, as the square root of 4 is 2.</p>
+many people from District 12. It doesn’t matter how many people the
+sample contains overall.</p>
+<p>The width of a confidence interval gets smaller as we collect more
+data, and it shrinks proportional to <span class="math inline">\frac{1}{\sqrt{n}}</span>, where n is the sample
+size.</p>
+<p>If we want the interval to be <strong>half as wide</strong>, we need
+<span class="math inline">\frac{1}{\sqrt{n}}</span> to be cut in half,
+which means n must become <strong>four times as large</strong>:</p>
+<p><span class="math display">
+\frac{1}{\sqrt{n_{\text{new}}}}
+= \frac{1}{\sqrt{4n}}
+= \frac{1}{2\sqrt{n}}
+\;\Longrightarrow\;
+n_{\text{new}} = 4n.
+</span></p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
@@ -671,6 +680,8 @@ <h2 id="problem-4">Problem 4</h2>
 <p>The data visualization below shows all Olympic gold medals for
 women’s gymnastics, broken down by the age of the gymnast.</p>
 <center><img src='../../assets/images/wi21-final/gymnastics.png' width=50%></center>
+<p><br></p>
+<h3 id="problem-4.1">Problem 4.1</h3>
 <p>Based on this data, rank the following three quantities in
 <strong>ascending</strong> order: the median age at which gold medals
 are earned, the mean age at which gold medals are earned, the standard
@@ -683,13 +694,13 @@ <h2 id="problem-4">Problem 4</h2>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse4" aria-expanded="true" aria-controls="collapse4">
+<h2 class="accordion-header" id="heading4_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse4_1" aria-expanded="true" aria-controls="collapse4_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse4" class="accordion-collapse collapse"
-aria-labelledby="heading4" data-bs-parent="#accordionExample">
+<div id="collapse4_1" class="accordion-collapse collapse"
+aria-labelledby="heading4_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -714,13 +725,50 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 </div>
+<p><br></p>
+<h3 id="problem-4.2">Problem 4.2</h3>
+<p>Which of the following is larger for this dataset?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> the difference between the 50th percentile of ages and the 25th
+percentile of ages</p></li>
+<li><p><input type="radio" disabled="" /> the difference between the 75th percentile of ages and the 50th
+percentile of ages</p></li>
+<li><p><input type="radio" disabled="" /> both are the same</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading4_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse4_2" aria-expanded="true" aria-controls="collapse4_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse4_2" class="accordion-collapse collapse"
+aria-labelledby="heading4_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> the difference between the 75th percentile
+of ages and the 50th percentile of ages</p>
+<p>Since the distribution is right skewed, the 75th percentile will have
+a larger difference from the 50th percentile than the 25th percentile.
+With right skewness, values above the 50th percentile will be more
+different than those smaller than the 50th percentile (and thus more
+spread out according to the graph). </p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>The
+average score on this problem was 78%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
 <hr />
 <h2 id="problem-5">Problem 5</h2>
 <p>The data visualization below shows all Olympic gold medals for
 women’s gymnastics, broken down by the age of the gymnast.</p>
 <center><img src='../../assets/images/wi21-final/gymnastics.png' width=50%></center>
-<p><br></p>
-<h3 id="problem-5.1">Problem 5.1</h3>
 <p>Based on this data, rank the following three quantities in
 <strong>ascending</strong> order: the median age at which gold medals
 are earned, the mean age at which gold medals are earned, the standard
@@ -733,13 +781,13 @@ <h3 id="problem-5.1">Problem 5.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading5_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_1" aria-expanded="true" aria-controls="collapse5_1">
+<h2 class="accordion-header" id="heading5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5" aria-expanded="true" aria-controls="collapse5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse5_1" class="accordion-collapse collapse"
-aria-labelledby="heading5_1" data-bs-parent="#accordionExample">
+<div id="collapse5" class="accordion-collapse collapse"
+aria-labelledby="heading5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -764,45 +812,6 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 </div>
-<p><br></p>
-<h3 id="problem-5.2">Problem 5.2</h3>
-<p>Which of the following is larger for this dataset?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> the difference between the 50th percentile of ages and the 25th
-percentile of ages</p></li>
-<li><p><input type="radio" disabled="" /> the difference between the 75th percentile of ages and the 50th
-percentile of ages</p></li>
-<li><p><input type="radio" disabled="" /> both are the same</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading5_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_2" aria-expanded="true" aria-controls="collapse5_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse5_2" class="accordion-collapse collapse"
-aria-labelledby="heading5_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> the difference between the 75th percentile
-of ages and the 50th percentile of ages</p>
-<p>Since the distribution is right skewed, the 75th percentile will have
-a larger difference from the 50th percentile than the 25th percentile.
-With right skewness, values above the 50th percentile will be more
-different than those smaller than the 50th percentile (and thus more
-spread out according to the graph). </p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>The
-average score on this problem was 78%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
 <hr />
 </body>
 </html>
diff --git a/docs/lectures/lec16/index.html b/docs/lectures/lec16/index.html
index 5febed3..2bf9141 100644
--- a/docs/lectures/lec16/index.html
+++ b/docs/lectures/lec16/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -1396,6 +1396,104 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-5">Problem 5</h2>
+<p>Suppose you have correctly implemented the function
+<code>area_between(x, y)</code> so that it returns the area under the
+armchair curve between <code>x</code> and <code>y</code>, assuming the
+inputs satisfy <code>-4 &lt;= x &lt;= y &lt;= 12</code>.</p>
+<p><strong>Note:</strong> You can still do this question, even if you
+didn’t know how to do the previous one.</p>
+<p><br></p>
+<h3 id="problem-5.1">Problem 5.1</h3>
+<p>What is the approximate value of
+<code>area_between(-2, 10)</code>?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> 1.9</p></li>
+<li><p><input type="radio" disabled="" /> 1.95</p></li>
+<li><p><input type="radio" disabled="" /> 1.975</p></li>
+<li><p><input type="radio" disabled="" /> 2</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading5_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_1" aria-expanded="true" aria-controls="collapse5_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse5_1" class="accordion-collapse collapse"
+aria-labelledby="heading5_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> 1.95</p>
+<p>The area we want to find is shown below in two colors. We can find
+the area in each half of the armchair curve separately and add the
+results.</p>
+<center><img src="../../assets/images/sp22-final/armchair-between-1.png" width="80%"/></center>
+<p>For the yellow area, we know that the area within 2 standard
+deviations of the mean on the standard normal curve is 0.95. The
+remaining 0.05 is split equally on both sides, so the yellow area is
+0.975.</p>
+<p>The blue area is the same by symmetry so the total shaded area is
+<span class="math inline">0.975*2 = 1.95</span>.</p>
+<p>Equivalently, we can use the fact that the total area under the
+armchair curve is 2, and the amount of unshaded area on either side is
+0.025, so the total shaded area is <span class="math inline">2 -
+(0.025*2) = 1.95.</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 76%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-5.2">Problem 5.2</h3>
+<p>What is the approximate value of
+<code>area_between(0.37, 8.37)</code>?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> 0.68</p></li>
+<li><p><input type="radio" disabled="" /> 0.95</p></li>
+<li><p><input type="radio" disabled="" /> 1</p></li>
+<li><p><input type="radio" disabled="" /> 1.5</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading5_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_2" aria-expanded="true" aria-controls="collapse5_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse5_2" class="accordion-collapse collapse"
+aria-labelledby="heading5_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> 1</p>
+<p>The area we want to find is shown below in two colors.</p>
+<center><img src="../../assets/images/sp22-final/armchair-between-2.png" width="80%"/></center>
+<p>As we saw in Problem 12.2, the point on the left half of the armchair
+curve that corresponds to 8.37 is 0.37. This means that if we move the
+blue area from the right half of the armchair curve to the left half, it
+will fit perfectly, as shown below.</p>
+<center><img src="../../assets/images/sp22-final/armchair-between-3.png" width="80%"/></center>
+<p>Therefore the total of the blue and yellow areas is the same as the
+area under one standard normal curve, which is 1.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 76%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-6">Problem 6</h2>
 <p>An IKEA chair designer is experimenting with some new ideas for
 armchair designs. She has the idea of making the arm rests shaped like
 bell curves, or normal distributions. A cross-section of the armchair
@@ -1435,17 +1533,17 @@ <h2 id="problem-5">Problem 5</h2>
 <span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a><span class="co">    Assume -4 &lt;= x &lt;= y &lt;= 12.&#39;&#39;&#39;</span></span>
 <span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> ___(c)___</span></code></pre></div>
 <p><br></p>
-<h3 id="problem-5.1">Problem 5.1</h3>
+<h3 id="problem-6.1">Problem 6.1</h3>
 <p>What goes in blank (a)?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading5_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_1" aria-expanded="true" aria-controls="collapse5_1">
+<h2 class="accordion-header" id="heading6_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse6_1" aria-expanded="true" aria-controls="collapse6_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse5_1" class="accordion-collapse collapse"
-aria-labelledby="heading5_1" data-bs-parent="#accordionExample">
+<div id="collapse6_1" class="accordion-collapse collapse"
+aria-labelledby="heading6_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1479,17 +1577,17 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-5.2">Problem 5.2</h3>
+<h3 id="problem-6.2">Problem 6.2</h3>
 <p>What goes in blank (b)?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading5_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_2" aria-expanded="true" aria-controls="collapse5_2">
+<h2 class="accordion-header" id="heading6_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse6_2" aria-expanded="true" aria-controls="collapse6_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse5_2" class="accordion-collapse collapse"
-aria-labelledby="heading5_2" data-bs-parent="#accordionExample">
+<div id="collapse6_2" class="accordion-collapse collapse"
+aria-labelledby="heading6_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1533,17 +1631,17 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-5.3">Problem 5.3</h3>
+<h3 id="problem-6.3">Problem 6.3</h3>
 <p>What goes in blank (c)?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading5_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5_3" aria-expanded="true" aria-controls="collapse5_3">
+<h2 class="accordion-header" id="heading6_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse6_3" aria-expanded="true" aria-controls="collapse6_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse5_3" class="accordion-collapse collapse"
-aria-labelledby="heading5_3" data-bs-parent="#accordionExample">
+<div id="collapse6_3" class="accordion-collapse collapse"
+aria-labelledby="heading6_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1568,104 +1666,6 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-6">Problem 6</h2>
-<p>Suppose you have correctly implemented the function
-<code>area_between(x, y)</code> so that it returns the area under the
-armchair curve between <code>x</code> and <code>y</code>, assuming the
-inputs satisfy <code>-4 &lt;= x &lt;= y &lt;= 12</code>.</p>
-<p><strong>Note:</strong> You can still do this question, even if you
-didn’t know how to do the previous one.</p>
-<p><br></p>
-<h3 id="problem-6.1">Problem 6.1</h3>
-<p>What is the approximate value of
-<code>area_between(-2, 10)</code>?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> 1.9</p></li>
-<li><p><input type="radio" disabled="" /> 1.95</p></li>
-<li><p><input type="radio" disabled="" /> 1.975</p></li>
-<li><p><input type="radio" disabled="" /> 2</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading6_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse6_1" aria-expanded="true" aria-controls="collapse6_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse6_1" class="accordion-collapse collapse"
-aria-labelledby="heading6_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> 1.95</p>
-<p>The area we want to find is shown below in two colors. We can find
-the area in each half of the armchair curve separately and add the
-results.</p>
-<center><img src="../../assets/images/sp22-final/armchair-between-1.png" width="80%"/></center>
-<p>For the yellow area, we know that the area within 2 standard
-deviations of the mean on the standard normal curve is 0.95. The
-remaining 0.05 is split equally on both sides, so the yellow area is
-0.975.</p>
-<p>The blue area is the same by symmetry so the total shaded area is
-<span class="math inline">0.975*2 = 1.95</span>.</p>
-<p>Equivalently, we can use the fact that the total area under the
-armchair curve is 2, and the amount of unshaded area on either side is
-0.025, so the total shaded area is <span class="math inline">2 -
-(0.025*2) = 1.95.</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 76%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-6.2">Problem 6.2</h3>
-<p>What is the approximate value of
-<code>area_between(0.37, 8.37)</code>?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> 0.68</p></li>
-<li><p><input type="radio" disabled="" /> 0.95</p></li>
-<li><p><input type="radio" disabled="" /> 1</p></li>
-<li><p><input type="radio" disabled="" /> 1.5</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading6_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse6_2" aria-expanded="true" aria-controls="collapse6_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse6_2" class="accordion-collapse collapse"
-aria-labelledby="heading6_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> 1</p>
-<p>The area we want to find is shown below in two colors.</p>
-<center><img src="../../assets/images/sp22-final/armchair-between-2.png" width="80%"/></center>
-<p>As we saw in Problem 12.2, the point on the left half of the armchair
-curve that corresponds to 8.37 is 0.37. This means that if we move the
-blue area from the right half of the armchair curve to the left half, it
-will fit perfectly, as shown below.</p>
-<center><img src="../../assets/images/sp22-final/armchair-between-3.png" width="80%"/></center>
-<p>Therefore the total of the blue and yellow areas is the same as the
-area under one standard normal curve, which is 1.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 76%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
 <p class="meta"><em>Source:</em> sp23-final — Q3</p>
 <h2 id="problem-7">Problem 7</h2>
 <p>This summer, Zoe wants to explore parts of the United States that she
@@ -2819,6 +2819,135 @@ <h5>Difficulty:
 </div>
 <hr />
 <h2 id="problem-13">Problem 13</h2>
+<p><br></p>
+<h3 id="problem-13.1">Problem 13.1</h3>
+<p>Recall that the mean points per game is 7, with a standard deviation
+of 5. Also note that for all players, points per game must be greater
+than or equal to 0.</p>
+<p>Using Chebyshev’s inequality, we find that at least <span
+class="math inline">p\%</span> of players scored 25 or fewer points per
+game.</p>
+<p>What is the value of <span class="math inline">p</span>? Give your
+answer as number between 0 and 100, rounded to 3 decimal places.</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading13_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse13_1" class="accordion-collapse collapse"
+aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> <span class="math inline">92.284\%</span></p>
+<p>Recall, Chebyshev’s inequality states that the proportion of values
+within <span class="math inline">z</span> standard deviations of the
+mean is <strong>at least</strong> <span class="math inline">1 -
+\frac{1}{z^2}</span>.</p>
+<p>To approach the problem, we’ll start by converting 25 points per game
+to standard units. Doing so yields <span class="math inline">\frac{25 -
+7}{5} = 3.6</span>. This means that 25 is 3.6 standard deviations
+<strong>above</strong> the mean. The value 3.6 standard deviations
+<strong>below</strong> the mean is <span class="math inline">7 - 3.6
+\cdot 5 = -11</span>, so when we use Chebyshev’s inequality with <span class="math inline">z = 3.6</span>, we will get a lower bound on the
+proportion of values between -11 and 25. However, as the question tells
+us, points per game must be non-negative, so in this case the proportion
+of values between -11 and 25 is the same as the proportion of values
+between 0 and 25 (i.e. the proportion of values less than or equal to
+25).</p>
+<p>When <span class="math inline">z = 3.6</span>, we have <span class="math inline">1 - \frac{1}{z^2} = 1 - \frac{1}{3.6^2} =
+0.922839</span>, which as a percentage rounded to three decimal places
+is <span class="math inline">92.284\%</span>. Thus, at least <span class="math inline">92.284\%</span> scored 25 or fewer points per
+game.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 46%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-13.2">Problem 13.2</h3>
+<p><span style="color:red"><b>Note: This problem is out of scope; it
+covers material no longer included in the course.</b></span></p>
+<p><strong>Note:</strong> This question uses the mathematical definition
+of percentile, not <code>np.percentile</code>.</p>
+<p>The array <code>aces</code> defined below contains the points per
+game scored by all members of the Las Vegas Aces. Note that it contains
+14 numbers that are in sorted order.</p>
+<div class="sourceCode" id="cb10"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>aces <span class="op">=</span> np.array([<span class="dv">0</span>, <span class="dv">0</span>, <span class="fl">1.05</span>, <span class="fl">1.47</span>, <span class="fl">1.96</span>, <span class="dv">2</span>, <span class="fl">3.25</span>, </span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>                 <span class="fl">10.53</span>, <span class="fl">11.09</span>, <span class="fl">11.62</span>, <span class="fl">12.19</span>, </span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>                 <span class="fl">14.24</span>, <span class="fl">14.81</span>, <span class="fl">18.25</span>])</span></code></pre></div>
+<p>As we saw in lab, percentiles are not unique. For instance, the
+number 1.05 is both the 15th percentile and 16th percentile of
+<code>aces</code>.</p>
+<p>There is a positive integer <span class="math inline">q</span>,
+between 0 and 100, such that 14.24 is the <span
+class="math inline">q</span>th percentile of <code>aces</code>, but
+14.81 is the <span class="math inline">(q+1)</span>th percentile of
+<code>aces</code>.</p>
+<p>What is the value of <span class="math inline">q</span>? Give your
+answer as an integer between 0 and 100.</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading13_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_2" aria-expanded="true" aria-controls="collapse13_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse13_2" class="accordion-collapse collapse"
+aria-labelledby="heading13_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> 85</p>
+<p>For reference, recall that we find the <span class="math inline">p</span>th percentile of a collection of <span class="math inline">n</span> numbers as follows:</p>
+<ol type="1">
+<li>Sort the collection in increasing order.</li>
+<li>Define <span class="math inline">h</span> to be <span class="math inline">p\%</span> of <span class="math inline">n</span>:</li>
+</ol>
+<p><span class="math display">h = \frac{p}{100} \cdot n</span></p>
+<ol start="3" type="1">
+<li><p>If <span class="math inline">h</span> is an integer, define <span class="math inline">k = h</span>. Otherwise, let <span class="math inline">k</span> be the smallest integer greater than <span class="math inline">h</span>.</p></li>
+<li><p>Take the <span class="math inline">k</span>th element of the
+sorted collection (start counting from 1, not 0).</p></li>
+</ol>
+<p><br/></p>
+<p>To start, it’s worth emphasizing that there are <span class="math inline">n = 14</span> numbers in <code>aces</code> total.
+14.24 is at position 12 (when the positions are numbered 1 through
+14).</p>
+<p>Let’s try and find a value of <span class="math inline">p</span> such
+that 14.24 is the <span class="math inline">p</span>th percentile. To do
+so, we might try and find what “percentage” of the way through the
+distribution 14.24 is; doing so gives <span class="math inline">\frac{12}{14} = 85.71\%</span>. If we follow the
+process outlined above with <span class="math inline">p = 85</span>, we
+get that <span class="math inline">h = \frac{85}{100} \cdot 14 =
+11.9</span> and thus <span class="math inline">k = 12</span>, meaning
+that the 85th percentile is the number at position 12, which 14.24.</p>
+<p>Let’s see what happens when we try the same process with <span class="math inline">p = 86</span>. This time, we have <span class="math inline">h = \frac{86}{100} \cdot 14 = 12.04</span> and thus
+<span class="math inline">k = 13</span>, meaning that the 86th
+percentile is the number at position 13, which is 14.81.</p>
+<p>This means that the value of <span class="math inline">q</span> is 85
+– the 85th percentile is 14.24, while the 86th percentile is 14.81.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 57%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-14">Problem 14</h2>
 <p>In addition to the <code>plum</code> DataFrame, we also have access
 to the <code>season</code> DataFrame, which contains statistics on all
 players in the WNBA in the 2021 season. The first few rows of
@@ -2837,7 +2966,7 @@ <h2 id="problem-13">Problem 13</h2>
 <p>Note that all of the numerical columns in <code>season</code> must
 contain values that are greater than or equal to 0.</p>
 <p><br></p>
-<h3 id="problem-13.1">Problem 13.1</h3>
+<h3 id="problem-14.1">Problem 14.1</h3>
 <p>Which of the following is the best choice for the index of
 <code>season</code>?</p>
 <ul class="task-list">
@@ -2848,13 +2977,13 @@ <h3 id="problem-13.1">Problem 13.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
+<h2 class="accordion-header" id="heading14_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_1" aria-expanded="true" aria-controls="collapse14_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_1" class="accordion-collapse collapse"
-aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
+<div id="collapse14_1" class="accordion-collapse collapse"
+aria-labelledby="heading14_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2877,7 +3006,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-14">Problem 14</h2>
+<h2 id="problem-15">Problem 15</h2>
 <p>In addition to the <code>plum</code> DataFrame, we also have access
 to the <code>season</code> DataFrame, which contains statistics on all
 players in the WNBA in the 2021 season. The first few rows of
@@ -2896,7 +3025,7 @@ <h2 id="problem-14">Problem 14</h2>
 <p>Note that all of the numerical columns in <code>season</code> must
 contain values that are greater than or equal to 0.</p>
 <p><br></p>
-<h3 id="problem-14.1">Problem 14.1</h3>
+<h3 id="problem-15.1">Problem 15.1</h3>
 <p>Which of the following is the best choice for the index of
 <code>season</code>?</p>
 <ul class="task-list">
@@ -2907,13 +3036,13 @@ <h3 id="problem-14.1">Problem 14.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_1" aria-expanded="true" aria-controls="collapse14_1">
+<h2 class="accordion-header" id="heading15_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_1" aria-expanded="true" aria-controls="collapse15_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_1" class="accordion-collapse collapse"
-aria-labelledby="heading14_1" data-bs-parent="#accordionExample">
+<div id="collapse15_1" class="accordion-collapse collapse"
+aria-labelledby="heading15_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2935,7 +3064,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.2">Problem 14.2</h3>
+<h3 id="problem-15.2">Problem 15.2</h3>
 <p><strong>Note:</strong> For the rest of the exam, assume that the
 index of <code>season</code> is still 0, 1, 2, 3, …</p>
 <p>Below is a histogram showing the distribution of the number of
@@ -2954,13 +3083,13 @@ <h3 id="problem-14.2">Problem 14.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_2" aria-expanded="true" aria-controls="collapse14_2">
+<h2 class="accordion-header" id="heading15_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_2" aria-expanded="true" aria-controls="collapse15_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_2" class="accordion-collapse collapse"
-aria-labelledby="heading14_2" data-bs-parent="#accordionExample">
+<div id="collapse15_2" class="accordion-collapse collapse"
+aria-labelledby="heading15_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2994,7 +3123,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.3">Problem 14.3</h3>
+<h3 id="problem-15.3">Problem 15.3</h3>
 <p>Sabrina Ionescu and Sami Whitcomb are both players on the New York
 Liberty, and are both California natives.</p>
 <p>In “original units”, Sabrina Ionescu had 3.5 turnovers per game. In
@@ -3006,13 +3135,13 @@ <h3 id="problem-14.3">Problem 14.3</h3>
 subpart that the mean number of turnovers per game is 1.25.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_3" aria-expanded="true" aria-controls="collapse14_3">
+<h2 class="accordion-header" id="heading15_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_3" aria-expanded="true" aria-controls="collapse15_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_3" class="accordion-collapse collapse"
-aria-labelledby="heading14_3" data-bs-parent="#accordionExample">
+<div id="collapse15_3" class="accordion-collapse collapse"
+aria-labelledby="heading15_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3059,19 +3188,19 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.4">Problem 14.4</h3>
+<h3 id="problem-15.4">Problem 15.4</h3>
 <p>What is the <strong>smallest</strong> possible number of turnovers
 per game, in <strong>standard units</strong>? Round your answer to 3
 decimal places.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_4" aria-expanded="true" aria-controls="collapse14_4">
+<h2 class="accordion-header" id="heading15_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_4" aria-expanded="true" aria-controls="collapse15_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_4" class="accordion-collapse collapse"
-aria-labelledby="heading14_4" data-bs-parent="#accordionExample">
+<div id="collapse15_4" class="accordion-collapse collapse"
+aria-labelledby="heading15_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3098,135 +3227,6 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-15">Problem 15</h2>
-<p><br></p>
-<h3 id="problem-15.1">Problem 15.1</h3>
-<p>Recall that the mean points per game is 7, with a standard deviation
-of 5. Also note that for all players, points per game must be greater
-than or equal to 0.</p>
-<p>Using Chebyshev’s inequality, we find that at least <span
-class="math inline">p\%</span> of players scored 25 or fewer points per
-game.</p>
-<p>What is the value of <span class="math inline">p</span>? Give your
-answer as number between 0 and 100, rounded to 3 decimal places.</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading15_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_1" aria-expanded="true" aria-controls="collapse15_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse15_1" class="accordion-collapse collapse"
-aria-labelledby="heading15_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> <span class="math inline">92.284\%</span></p>
-<p>Recall, Chebyshev’s inequality states that the proportion of values
-within <span class="math inline">z</span> standard deviations of the
-mean is <strong>at least</strong> <span class="math inline">1 -
-\frac{1}{z^2}</span>.</p>
-<p>To approach the problem, we’ll start by converting 25 points per game
-to standard units. Doing so yields <span class="math inline">\frac{25 -
-7}{5} = 3.6</span>. This means that 25 is 3.6 standard deviations
-<strong>above</strong> the mean. The value 3.6 standard deviations
-<strong>below</strong> the mean is <span class="math inline">7 - 3.6
-\cdot 5 = -11</span>, so when we use Chebyshev’s inequality with <span class="math inline">z = 3.6</span>, we will get a lower bound on the
-proportion of values between -11 and 25. However, as the question tells
-us, points per game must be non-negative, so in this case the proportion
-of values between -11 and 25 is the same as the proportion of values
-between 0 and 25 (i.e. the proportion of values less than or equal to
-25).</p>
-<p>When <span class="math inline">z = 3.6</span>, we have <span class="math inline">1 - \frac{1}{z^2} = 1 - \frac{1}{3.6^2} =
-0.922839</span>, which as a percentage rounded to three decimal places
-is <span class="math inline">92.284\%</span>. Thus, at least <span class="math inline">92.284\%</span> scored 25 or fewer points per
-game.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 46%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-15.2">Problem 15.2</h3>
-<p><span style="color:red"><b>Note: This problem is out of scope; it
-covers material no longer included in the course.</b></span></p>
-<p><strong>Note:</strong> This question uses the mathematical definition
-of percentile, not <code>np.percentile</code>.</p>
-<p>The array <code>aces</code> defined below contains the points per
-game scored by all members of the Las Vegas Aces. Note that it contains
-14 numbers that are in sorted order.</p>
-<div class="sourceCode" id="cb10"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>aces <span class="op">=</span> np.array([<span class="dv">0</span>, <span class="dv">0</span>, <span class="fl">1.05</span>, <span class="fl">1.47</span>, <span class="fl">1.96</span>, <span class="dv">2</span>, <span class="fl">3.25</span>, </span>
-<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>                 <span class="fl">10.53</span>, <span class="fl">11.09</span>, <span class="fl">11.62</span>, <span class="fl">12.19</span>, </span>
-<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>                 <span class="fl">14.24</span>, <span class="fl">14.81</span>, <span class="fl">18.25</span>])</span></code></pre></div>
-<p>As we saw in lab, percentiles are not unique. For instance, the
-number 1.05 is both the 15th percentile and 16th percentile of
-<code>aces</code>.</p>
-<p>There is a positive integer <span class="math inline">q</span>,
-between 0 and 100, such that 14.24 is the <span
-class="math inline">q</span>th percentile of <code>aces</code>, but
-14.81 is the <span class="math inline">(q+1)</span>th percentile of
-<code>aces</code>.</p>
-<p>What is the value of <span class="math inline">q</span>? Give your
-answer as an integer between 0 and 100.</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading15_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_2" aria-expanded="true" aria-controls="collapse15_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse15_2" class="accordion-collapse collapse"
-aria-labelledby="heading15_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> 85</p>
-<p>For reference, recall that we find the <span class="math inline">p</span>th percentile of a collection of <span class="math inline">n</span> numbers as follows:</p>
-<ol type="1">
-<li>Sort the collection in increasing order.</li>
-<li>Define <span class="math inline">h</span> to be <span class="math inline">p\%</span> of <span class="math inline">n</span>:</li>
-</ol>
-<p><span class="math display">h = \frac{p}{100} \cdot n</span></p>
-<ol start="3" type="1">
-<li><p>If <span class="math inline">h</span> is an integer, define <span class="math inline">k = h</span>. Otherwise, let <span class="math inline">k</span> be the smallest integer greater than <span class="math inline">h</span>.</p></li>
-<li><p>Take the <span class="math inline">k</span>th element of the
-sorted collection (start counting from 1, not 0).</p></li>
-</ol>
-<p><br/></p>
-<p>To start, it’s worth emphasizing that there are <span class="math inline">n = 14</span> numbers in <code>aces</code> total.
-14.24 is at position 12 (when the positions are numbered 1 through
-14).</p>
-<p>Let’s try and find a value of <span class="math inline">p</span> such
-that 14.24 is the <span class="math inline">p</span>th percentile. To do
-so, we might try and find what “percentage” of the way through the
-distribution 14.24 is; doing so gives <span class="math inline">\frac{12}{14} = 85.71\%</span>. If we follow the
-process outlined above with <span class="math inline">p = 85</span>, we
-get that <span class="math inline">h = \frac{85}{100} \cdot 14 =
-11.9</span> and thus <span class="math inline">k = 12</span>, meaning
-that the 85th percentile is the number at position 12, which 14.24.</p>
-<p>Let’s see what happens when we try the same process with <span class="math inline">p = 86</span>. This time, we have <span class="math inline">h = \frac{86}{100} \cdot 14 = 12.04</span> and thus
-<span class="math inline">k = 13</span>, meaning that the 86th
-percentile is the number at position 13, which is 14.81.</p>
-<p>This means that the value of <span class="math inline">q</span> is 85
-– the 85th percentile is 14.24, while the 86th percentile is 14.81.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 57%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
 <p class="meta"><em>Source:</em> wi24-final — Q14</p>
 <h2 id="problem-16">Problem 16</h2>
 <p><br></p>
diff --git a/docs/lectures/lec17/index.html b/docs/lectures/lec17/index.html
index 631360d..727b6b0 100644
--- a/docs/lectures/lec17/index.html
+++ b/docs/lectures/lec17/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -2097,48 +2097,12 @@ <h5>Difficulty:
 <p><br></p>
 <hr />
 <h2 id="problem-10">Problem 10</h2>
-<p><strong>True or False</strong>: Suppose that from a sample, you
-compute a 95% normal confidence interval for a population parameter to
-be the interval [L, R]. Then the average of L and R is the mean of the
-original sample.</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading10">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10" aria-expanded="true" aria-controls="collapse10">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse10" class="accordion-collapse collapse"
-aria-labelledby="heading10" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> True</p>
-<p>True, a 95% confidence interval indicates we are 95% confident that
-the true population parameter falls within the interval [L, R]. Looking
-at how a confidence interval is calculated is by adding/ subtracting a
-confidence level value (z) by the standard error. Since the top and
-bottom of the interval will be different from the mean by the same
-amount, the average will be the mean. (For more information, refer to
-the reference sheet)</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 68%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-11">Problem 11</h2>
 <p>From a population with mean 500 and standard deviation 50, you
 collect a sample of size 100. The sample has mean 400 and standard
 deviation 40. You bootstrap this sample 10,000 times, collecting 10,000
 resample means.</p>
 <p><br></p>
-<h3 id="problem-11.1">Problem 11.1</h3>
+<h3 id="problem-10.1">Problem 10.1</h3>
 <p>Which of the following is the most accurate description of the mean
 of the distribution of the 10,000 bootstrapped means?</p>
 <ul class="task-list">
@@ -2149,13 +2113,13 @@ <h3 id="problem-11.1">Problem 11.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_1" aria-expanded="true" aria-controls="collapse11_1">
+<h2 class="accordion-header" id="heading10_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_1" aria-expanded="true" aria-controls="collapse10_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_1" class="accordion-collapse collapse"
-aria-labelledby="heading11_1" data-bs-parent="#accordionExample">
+<div id="collapse10_1" class="accordion-collapse collapse"
+aria-labelledby="heading10_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2176,7 +2140,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.2">Problem 11.2</h3>
+<h3 id="problem-10.2">Problem 10.2</h3>
 <p>Which of the following is closest to the standard deviation of the
 distribution of the 10,000 bootstrapped means?</p>
 <ul class="task-list">
@@ -2187,13 +2151,13 @@ <h3 id="problem-11.2">Problem 11.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_2" aria-expanded="true" aria-controls="collapse11_2">
+<h2 class="accordion-header" id="heading10_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_2" aria-expanded="true" aria-controls="collapse10_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_2" class="accordion-collapse collapse"
-aria-labelledby="heading11_2" data-bs-parent="#accordionExample">
+<div id="collapse10_2" class="accordion-collapse collapse"
+aria-labelledby="heading10_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2213,7 +2177,50 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-11">Problem 11</h2>
+<p><strong>True or False</strong>: Suppose that from a sample, you
+compute a 95% normal confidence interval for a population parameter to
+be the interval [L, R]. Then the average of L and R is the mean of the
+original sample.</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading11">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11" aria-expanded="true" aria-controls="collapse11">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse11" class="accordion-collapse collapse"
+aria-labelledby="heading11" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> True</p>
+<p>True, a 95% confidence interval indicates we are 95% confident that
+the true population parameter falls within the interval [L, R]. Looking
+at how a confidence interval is calculated is by adding/ subtracting a
+confidence level value (z) by the standard error. Since the top and
+bottom of the interval will be different from the mean by the same
+amount, the average will be the mean. (For more information, refer to
+the reference sheet)</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 68%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <h2 id="problem-12">Problem 12</h2>
+<p>The <code>season</code> DataFrame contains statistics on all players
+in the WNBA in the 2021 season. The first few rows of
+<code>season</code> are shown below.</p>
+<center><img src='../../assets/images/wi22-final/seasons.png' width=40%></center>
+<p>Each row in <code>season</code> corresponds to a single player. In
+this problem, we’ll be working with the <code>'PPG'</code> column, which
+contains the number of points scored per game played.</p>
 <p>Suppose we only have access to the DataFrame
 <code>small_season</code>, which is a random sample of <strong>size
 36</strong> from <code>season</code>. We’re interested in learning about
@@ -2384,122 +2391,75 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<hr />
-<h2 id="problem-13">Problem 13</h2>
-<p>Answer the following questions about a basketball dataset.</p>
-<p><br></p>
-<h3 id="problem-13.1">Problem 13.1</h3>
-<p>Suppose you have a random sample of 36 games in a basketball season.
-In your sample, the mean number of points per game is 9, with a standard
-deviation of 4 points per game. Using only this information, compute a
-95% confidence interval for the true mean points per game in that
-season. What are the left and right endpoints of your interval?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading13_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse13_1" class="accordion-collapse collapse"
-aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> <span class="math inline">[7.667,
-10.333]</span></p>
-<p>In a normal distribution, roughly 95% of values are within 2 standard
-deviations of the mean. The CLT tells us that the distribution of sample
-means is roughly normal, and in subpart 4 of this problem we already
-computed the SD of the distribution of sample means to be <span class="math inline">\frac{2}{3}</span>.</p>
-<p>So, our normal-based 95% confidence interval is computed as
-follows:</p>
-<p><span class="math display">\begin{aligned} &amp;[\text{mean of
-sample} - 2 \cdot \text{SD of distribution of sample means}, \text{mean
-of sample} + 2 \cdot \text{SD of distribution of sample means}] \\
-&amp;= [9 - 2 \cdot \frac{4}{\sqrt{36}}, 9 + 2 \cdot
-\frac{4}{\sqrt{36}}] \\ &amp;= [9 - \frac{4}{3}, 9 + \frac{4}{3}] \\
-&amp;\approx \boxed{[7.667, 10.333]} \end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 87%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-13.2">Problem 13.2</h3>
-<p>It turns out that the true mean number of points per game in that
-season was 7, which is not in the interval you found above (if it is,
-check your work!). Select the true statement below.</p>
+<h3 id="problem-12.4">Problem 12.4</h3>
+<p>We construct a 95% confidence interval for the true mean points per
+game for all players by taking the middle 95% of the bootstrapped sample
+means.</p>
+<div class="sourceCode" id="cb12"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>left_b <span class="op">=</span> np.percentile(boot_means, <span class="fl">2.5</span>)</span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>right_b <span class="op">=</span> np.percentile(boot_means, <span class="fl">97.5</span>)</span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>boot_ci <span class="op">=</span> [left_b, right_b]</span></code></pre></div>
+<p>Select the most correct statement below.</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
-not contain the true mean points per game, which means that the
-distribution of the sample mean is not normal.</p></li>
-<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
-not contain the true mean points per game, which means that the
-distribution of points per game in <code>small_season</code> is not
-normal.</p></li>
-<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
-not contain the true mean points per game. This is to be expected,
-because the Central Limit Theorem is only correct 95% of the time.</p></li>
-<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
-not contain the true mean points per game, but if we collected many
-original samples and constructed many 95% confidence intervals, then
-roughly 95% of them would contain the true mean points per game.</p></li>
-<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
-not contain the true mean points per game, but if we collected many
-original samples and constructed many 95% confidence intervals, then
-exactly 95% of them would contain the true mean points per game.</p></li>
+<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is exactly equal to the mean
+points per game in <code>season</code>.</p></li>
+<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is not necessarily equal to the
+mean points per game in <code>season</code>, but is close.</p></li>
+<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is exactly equal to the mean
+points per game in <code>small_season</code>.</p></li>
+<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is not necessarily equal to the
+mean points per game in <code>small_season</code>, but is close.</p></li>
+<li><p><input type="radio" disabled="" /> <code>(left_b _+ right_b) / 2</code> is not close to either the mean
+points per game in <code>season</code> or the mean points per game in
+<code>small_season</code>.</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_2" aria-expanded="true" aria-controls="collapse13_2">
+<h2 class="accordion-header" id="heading12_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_4" aria-expanded="true" aria-controls="collapse12_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_2" class="accordion-collapse collapse"
-aria-labelledby="heading13_2" data-bs-parent="#accordionExample">
+<div id="collapse12_4" class="accordion-collapse collapse"
+aria-labelledby="heading12_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> The 95% confidence interval we created in
-the previous subpart did not contain the true mean points per game, but
-if we collected many original samples and constructed many 95%
-confidence intervals, then roughly 95% of them would contain the true
-mean points per game.</p>
-<p>In a confidence interval, the confidence level gives us a level of
-confidence in <strong>the process</strong> used to create the confidence
-interval. If we repeat the process of collecting a sample from the
-population and using the sample to construct a c% confidence interval
-for the population mean, then <strong>roughly</strong> c% of the
-intervals we create should contain the population mean. Option 4 is the
-only option that corresponds to this interpretation; the others are all
-incorrect in different ways.</p>
+<p><strong>Answer:</strong> <code>(left_b + right_b) / 2</code> is not
+necessarily equal to the mean points per game in
+<code>small_season</code>, but is close.</p>
+<p>Normal-based confidence intervals are of the form <span class="math inline">[\text{mean} - \text{something}, \text{mean} +
+\text{something}]</span>. In such confidence intervals, it is the case
+that the average of the left and right endpoints is exactly the mean of
+the distribution used to compute the interval.</p>
+<p>However, <strong>the confidence interval we’ve created is not
+normal-based</strong>, rather it is bootstrap-based! As such, we can’t
+say that anything is <em>exactly</em> true; this rules out Options 1 and
+3.</p>
+<p>Our 95% confidence interval was created by taking the middle 95% of
+bootstrapped sample means. The distribution of bootstrapped sample means
+is <strong>roughly</strong> normal, and the normal distribution is
+symmetric (the mean and median are both equal, and represent the
+“center” of the distribution). This means that the middle of our 95%
+confidence interval should be roughly equal to the mean of the
+distribution of bootstrapped sample means. This implies that Option 4 is
+correct; the difference between Options 2 and 4 is that Option 4 uses
+<code>small_season</code>, which is the sample we bootstrapped from,
+while Option 2 uses <code>season</code>, which was not accessed at all
+in our bootstrapping procedure.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 87%.</p>
+<p>The average score on this problem was 62%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-14">Problem 14</h2>
-<p>The <code>season</code> DataFrame contains statistics on all players
-in the WNBA in the 2021 season. The first few rows of
-<code>season</code> are shown below.</p>
-<center><img src='../../assets/images/wi22-final/seasons.png' width=40%></center>
-<p>Each row in <code>season</code> corresponds to a single player. In
-this problem, we’ll be working with the <code>'PPG'</code> column, which
-contains the number of points scored per game played.</p>
+<h2 id="problem-13">Problem 13</h2>
 <p>Suppose we only have access to the DataFrame
 <code>small_season</code>, which is a random sample of <strong>size
 36</strong> from <code>season</code>. We’re interested in learning about
@@ -2509,19 +2469,19 @@ <h2 id="problem-14">Problem 14</h2>
 and compute the mean of the resample each time. We want to store these
 10,000 bootstrapped means in the array <code>boot_means</code>.</p>
 <p>Here is a broken implementation of this procedure.</p>
-<div class="sourceCode" id="cb12"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>boot_means <span class="op">=</span> np.array([])                                           </span>
-<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(<span class="dv">10000</span>):                                          </span>
-<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>    resample <span class="op">=</span> small_season.sample(season.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)  <span class="co"># Line 1</span></span>
-<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>    resample_mean <span class="op">=</span> small_season.get(<span class="st">&#39;PPG&#39;</span>).mean()                  <span class="co"># Line 2</span></span>
-<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>    np.append(boot_means, new_mean)                                 <span class="co"># Line 3</span></span></code></pre></div>
+<div class="sourceCode" id="cb13"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>boot_means <span class="op">=</span> np.array([])                                           </span>
+<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(<span class="dv">10000</span>):                                          </span>
+<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>    resample <span class="op">=</span> small_season.sample(season.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)  <span class="co"># Line 1</span></span>
+<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>    resample_mean <span class="op">=</span> small_season.get(<span class="st">&#39;PPG&#39;</span>).mean()                  <span class="co"># Line 2</span></span>
+<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>    np.append(boot_means, new_mean)                                 <span class="co"># Line 3</span></span></code></pre></div>
 <p>For each of the 3 lines of code above (marked by comments), specify
 what is incorrect about the line by selecting one or more of the
 corresponding options below. Or, select “Line _ is correct as-is” if you
 believe there’s nothing that needs to be changed about the line in order
 for the above code to run properly.</p>
 <p><br></p>
-<h3 id="problem-14.1">Problem 14.1</h3>
+<h3 id="problem-13.1">Problem 13.1</h3>
 <p>What is incorrect about Line 1? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> Currently the procedure samples from <code>small_season</code>, when
@@ -2534,13 +2494,13 @@ <h3 id="problem-14.1">Problem 14.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_1" aria-expanded="true" aria-controls="collapse14_1">
+<h2 class="accordion-header" id="heading13_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_1" class="accordion-collapse collapse"
-aria-labelledby="heading14_1" data-bs-parent="#accordionExample">
+<div id="collapse13_1" class="accordion-collapse collapse"
+aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2571,7 +2531,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.2">Problem 14.2</h3>
+<h3 id="problem-13.2">Problem 13.2</h3>
 <p>What is incorrect about Line 2? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> Currently it is taking the mean of the <code>'PPG'</code> column in
@@ -2586,13 +2546,13 @@ <h3 id="problem-14.2">Problem 14.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_2" aria-expanded="true" aria-controls="collapse14_2">
+<h2 class="accordion-header" id="heading13_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_2" aria-expanded="true" aria-controls="collapse13_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_2" class="accordion-collapse collapse"
-aria-labelledby="heading14_2" data-bs-parent="#accordionExample">
+<div id="collapse13_2" class="accordion-collapse collapse"
+aria-labelledby="heading13_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2619,7 +2579,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.3">Problem 14.3</h3>
+<h3 id="problem-13.3">Problem 13.3</h3>
 <p>What is incorrect about Line 3? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> The result of calling <code>np.append</code> is not being reassigned
@@ -2634,13 +2594,13 @@ <h3 id="problem-14.3">Problem 14.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading14_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_3" aria-expanded="true" aria-controls="collapse14_3">
+<h2 class="accordion-header" id="heading13_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_3" aria-expanded="true" aria-controls="collapse13_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse14_3" class="accordion-collapse collapse"
-aria-labelledby="heading14_3" data-bs-parent="#accordionExample">
+<div id="collapse13_3" class="accordion-collapse collapse"
+aria-labelledby="heading13_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2670,75 +2630,8 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-14.4">Problem 14.4</h3>
-<p>We construct a 95% confidence interval for the true mean points per
-game for all players by taking the middle 95% of the bootstrapped sample
-means.</p>
-<div class="sourceCode" id="cb13"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>left_b <span class="op">=</span> np.percentile(boot_means, <span class="fl">2.5</span>)</span>
-<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>right_b <span class="op">=</span> np.percentile(boot_means, <span class="fl">97.5</span>)</span>
-<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>boot_ci <span class="op">=</span> [left_b, right_b]</span></code></pre></div>
-<p>Select the most correct statement below.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is exactly equal to the mean
-points per game in <code>season</code>.</p></li>
-<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is not necessarily equal to the
-mean points per game in <code>season</code>, but is close.</p></li>
-<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is exactly equal to the mean
-points per game in <code>small_season</code>.</p></li>
-<li><p><input type="radio" disabled="" /> <code>(left_b + right_b) / 2</code> is not necessarily equal to the
-mean points per game in <code>small_season</code>, but is close.</p></li>
-<li><p><input type="radio" disabled="" /> <code>(left_b _+ right_b) / 2</code> is not close to either the mean
-points per game in <code>season</code> or the mean points per game in
-<code>small_season</code>.</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading14_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_4" aria-expanded="true" aria-controls="collapse14_4">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse14_4" class="accordion-collapse collapse"
-aria-labelledby="heading14_4" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> <code>(left_b + right_b) / 2</code> is not
-necessarily equal to the mean points per game in
-<code>small_season</code>, but is close.</p>
-<p>Normal-based confidence intervals are of the form <span class="math inline">[\text{mean} - \text{something}, \text{mean} +
-\text{something}]</span>. In such confidence intervals, it is the case
-that the average of the left and right endpoints is exactly the mean of
-the distribution used to compute the interval.</p>
-<p>However, <strong>the confidence interval we’ve created is not
-normal-based</strong>, rather it is bootstrap-based! As such, we can’t
-say that anything is <em>exactly</em> true; this rules out Options 1 and
-3.</p>
-<p>Our 95% confidence interval was created by taking the middle 95% of
-bootstrapped sample means. The distribution of bootstrapped sample means
-is <strong>roughly</strong> normal, and the normal distribution is
-symmetric (the mean and median are both equal, and represent the
-“center” of the distribution). This means that the middle of our 95%
-confidence interval should be roughly equal to the mean of the
-distribution of bootstrapped sample means. This implies that Option 4 is
-correct; the difference between Options 2 and 4 is that Option 4 uses
-<code>small_season</code>, which is the sample we bootstrapped from,
-while Option 2 uses <code>season</code>, which was not accessed at all
-in our bootstrapping procedure.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 62%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
 <hr />
-<h2 id="problem-15">Problem 15</h2>
+<h2 id="problem-14">Problem 14</h2>
 <p>For your convenience, we show the first few rows of
 <code>season</code> again below.</p>
 <center><img src='../../assets/images/wi22-final/seasons.png' width=40%></center>
@@ -2765,7 +2658,7 @@ <h2 id="problem-15">Problem 15</h2>
 believe there’s nothing that needs to be changed about the line in order
 for the above code to run properly.</p>
 <p><br></p>
-<h3 id="problem-15.1">Problem 15.1</h3>
+<h3 id="problem-14.1">Problem 14.1</h3>
 <p>What is incorrect about Line 1? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> Currently the procedure samples from <code>small_season</code>, when
@@ -2778,13 +2671,13 @@ <h3 id="problem-15.1">Problem 15.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_1" aria-expanded="true" aria-controls="collapse15_1">
+<h2 class="accordion-header" id="heading14_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_1" aria-expanded="true" aria-controls="collapse14_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_1" class="accordion-collapse collapse"
-aria-labelledby="heading15_1" data-bs-parent="#accordionExample">
+<div id="collapse14_1" class="accordion-collapse collapse"
+aria-labelledby="heading14_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2815,7 +2708,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.2">Problem 15.2</h3>
+<h3 id="problem-14.2">Problem 14.2</h3>
 <p>What is incorrect about Line 2? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> Currently it is taking the mean of the <code>'PPG'</code> column in
@@ -2830,13 +2723,13 @@ <h3 id="problem-15.2">Problem 15.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_2" aria-expanded="true" aria-controls="collapse15_2">
+<h2 class="accordion-header" id="heading14_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_2" aria-expanded="true" aria-controls="collapse14_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_2" class="accordion-collapse collapse"
-aria-labelledby="heading15_2" data-bs-parent="#accordionExample">
+<div id="collapse14_2" class="accordion-collapse collapse"
+aria-labelledby="heading14_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2863,7 +2756,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.3">Problem 15.3</h3>
+<h3 id="problem-14.3">Problem 14.3</h3>
 <p>What is incorrect about Line 3? Select all that apply.</p>
 <ul class="task-list">
 <li><p><input type="checkbox" disabled="" /> The result of calling <code>np.append</code> is not being reassigned
@@ -2878,13 +2771,13 @@ <h3 id="problem-15.3">Problem 15.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_3" aria-expanded="true" aria-controls="collapse15_3">
+<h2 class="accordion-header" id="heading14_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_3" aria-expanded="true" aria-controls="collapse14_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_3" class="accordion-collapse collapse"
-aria-labelledby="heading15_3" data-bs-parent="#accordionExample">
+<div id="collapse14_3" class="accordion-collapse collapse"
+aria-labelledby="heading14_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2914,7 +2807,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.4">Problem 15.4</h3>
+<h3 id="problem-14.4">Problem 14.4</h3>
 <p>Suppose we’ve now fixed everything that was incorrect about our
 bootstrapping implementation.</p>
 <p>Recall from earlier in the exam that, in <code>season</code>, the
@@ -2935,13 +2828,13 @@ <h3 id="problem-15.4">Problem 15.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_4" aria-expanded="true" aria-controls="collapse15_4">
+<h2 class="accordion-header" id="heading14_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_4" aria-expanded="true" aria-controls="collapse14_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_4" class="accordion-collapse collapse"
-aria-labelledby="heading15_4" data-bs-parent="#accordionExample">
+<div id="collapse14_4" class="accordion-collapse collapse"
+aria-labelledby="heading14_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2989,7 +2882,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.5">Problem 15.5</h3>
+<h3 id="problem-14.5">Problem 14.5</h3>
 <p>We construct a 95% confidence interval for the true mean points per
 game for all players by taking the middle 95% of the bootstrapped sample
 means.</p>
@@ -3013,13 +2906,13 @@ <h3 id="problem-15.5">Problem 15.5</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_5" aria-expanded="true" aria-controls="collapse15_5">
+<h2 class="accordion-header" id="heading14_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_5" aria-expanded="true" aria-controls="collapse14_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_5" class="accordion-collapse collapse"
-aria-labelledby="heading15_5" data-bs-parent="#accordionExample">
+<div id="collapse14_5" class="accordion-collapse collapse"
+aria-labelledby="heading14_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3056,7 +2949,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.6">Problem 15.6</h3>
+<h3 id="problem-14.6">Problem 14.6</h3>
 <p>Instead of bootstrapping, we could also construct a 95% confidence
 interval for the true mean points per game by using the Central Limit
 Theorem.</p>
@@ -3072,13 +2965,13 @@ <h3 id="problem-15.6">Problem 15.6</h3>
 answers as numbers rounded to 3 decimal places.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_6">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_6" aria-expanded="true" aria-controls="collapse15_6">
+<h2 class="accordion-header" id="heading14_6">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_6" aria-expanded="true" aria-controls="collapse14_6">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_6" class="accordion-collapse collapse"
-aria-labelledby="heading15_6" data-bs-parent="#accordionExample">
+<div id="collapse14_6" class="accordion-collapse collapse"
+aria-labelledby="heading14_6" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3107,7 +3000,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-15.7">Problem 15.7</h3>
+<h3 id="problem-14.7">Problem 14.7</h3>
 <p>Recall that the mean points per game in <code>season</code> is 7,
 which is not in the interval you found above (if it is, check your
 work!).</p>
@@ -3134,13 +3027,120 @@ <h3 id="problem-15.7">Problem 15.7</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading15_7">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_7" aria-expanded="true" aria-controls="collapse15_7">
+<h2 class="accordion-header" id="heading14_7">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse14_7" aria-expanded="true" aria-controls="collapse14_7">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse15_7" class="accordion-collapse collapse"
-aria-labelledby="heading15_7" data-bs-parent="#accordionExample">
+<div id="collapse14_7" class="accordion-collapse collapse"
+aria-labelledby="heading14_7" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> The 95% confidence interval we created in
+the previous subpart did not contain the true mean points per game, but
+if we collected many original samples and constructed many 95%
+confidence intervals, then roughly 95% of them would contain the true
+mean points per game.</p>
+<p>In a confidence interval, the confidence level gives us a level of
+confidence in <strong>the process</strong> used to create the confidence
+interval. If we repeat the process of collecting a sample from the
+population and using the sample to construct a c% confidence interval
+for the population mean, then <strong>roughly</strong> c% of the
+intervals we create should contain the population mean. Option 4 is the
+only option that corresponds to this interpretation; the others are all
+incorrect in different ways.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 87%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-15">Problem 15</h2>
+<p>Answer the following questions about a basketball dataset.</p>
+<p><br></p>
+<h3 id="problem-15.1">Problem 15.1</h3>
+<p>Suppose you have a random sample of 36 games in a basketball season.
+In your sample, the mean number of points per game is 9, with a standard
+deviation of 4 points per game. Using only this information, compute a
+95% confidence interval for the true mean points per game in that
+season. What are the left and right endpoints of your interval?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading15_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_1" aria-expanded="true" aria-controls="collapse15_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse15_1" class="accordion-collapse collapse"
+aria-labelledby="heading15_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> <span class="math inline">[7.667,
+10.333]</span></p>
+<p>In a normal distribution, roughly 95% of values are within 2 standard
+deviations of the mean. The CLT tells us that the distribution of sample
+means is roughly normal, and in subpart 4 of this problem we already
+computed the SD of the distribution of sample means to be <span class="math inline">\frac{2}{3}</span>.</p>
+<p>So, our normal-based 95% confidence interval is computed as
+follows:</p>
+<p><span class="math display">\begin{aligned} &amp;[\text{mean of
+sample} - 2 \cdot \text{SD of distribution of sample means}, \text{mean
+of sample} + 2 \cdot \text{SD of distribution of sample means}] \\
+&amp;= [9 - 2 \cdot \frac{4}{\sqrt{36}}, 9 + 2 \cdot
+\frac{4}{\sqrt{36}}] \\ &amp;= [9 - \frac{4}{3}, 9 + \frac{4}{3}] \\
+&amp;\approx \boxed{[7.667, 10.333]} \end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 87%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-15.2">Problem 15.2</h3>
+<p>It turns out that the true mean number of points per game in that
+season was 7, which is not in the interval you found above (if it is,
+check your work!). Select the true statement below.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
+not contain the true mean points per game, which means that the
+distribution of the sample mean is not normal.</p></li>
+<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
+not contain the true mean points per game, which means that the
+distribution of points per game in <code>small_season</code> is not
+normal.</p></li>
+<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
+not contain the true mean points per game. This is to be expected,
+because the Central Limit Theorem is only correct 95% of the time.</p></li>
+<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
+not contain the true mean points per game, but if we collected many
+original samples and constructed many 95% confidence intervals, then
+roughly 95% of them would contain the true mean points per game.</p></li>
+<li><p><input type="radio" disabled="" /> The 95% confidence interval we created in the previous subpart did
+not contain the true mean points per game, but if we collected many
+original samples and constructed many 95% confidence intervals, then
+exactly 95% of them would contain the true mean points per game.</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading15_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse15_2" aria-expanded="true" aria-controls="collapse15_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse15_2" class="accordion-collapse collapse"
+aria-labelledby="heading15_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
diff --git a/docs/lectures/lec18/index.html b/docs/lectures/lec18/index.html
index 65b2c69..7239f38 100644
--- a/docs/lectures/lec18/index.html
+++ b/docs/lectures/lec18/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -602,83 +602,6 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-4">Problem 4</h2>
-<p>Suppose you draw a sample of size 100 from a population with mean 50
-and standard deviation 15. What is the probability that your sample has
-a mean between 50 and 53? Input the probability below, as a number
-between 0 and 1, rounded to <strong>two decimal places</strong>.</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse4" aria-expanded="true" aria-controls="collapse4">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse4" class="accordion-collapse collapse"
-aria-labelledby="heading4" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> 0.48</p>
-<p>This problem is testing our understanding of the Central Limit
-Theorem and normal distributions. Recall, the Central Limit Theorem
-tells us that the distribution of the sample mean is roughly normal,
-with the following characteristics:</p>
-<p><span class="math display">\begin{align*}
-\text{Mean of Distribution of Possible Sample Means} &amp;=
-\text{Population Mean} = 50 \\
-\text{SD of Distribution of Possible Sample Means} &amp;=
-\frac{\text{Population SD}}{\sqrt{\text{Sample Size}}} =
-\frac{15}{\sqrt{100}} = 1.5
-\end{align*}
-</span></p>
-<p>Given this information, it may be easier to express the problem as
-“We draw a value from a normal distribution with mean 50 and SD 1.5.
-What is the probability that the value is between 50 and 53?” Note that
-this probability is equal to the <strong>proportion of values between 50
-and 53</strong> in a normal distribution whose mean is 50 and 1.5 (since
-probabilities can be thought of as proportions).</p>
-<p>In class, we typically worked with the <em>standard</em> normal
-distribution, in which the mean was 0, the SD was 1, and the <span class="math inline">x</span>-axis represented values in standard units.
-Let’s convert the quantities of interest in this problem to standard
-units, keeping in mind that the mean and SD we’re using now are the mean
-and SD of the distribution of possible sample means, not of the
-population.</p>
-<ul>
-<li>50 converted to standard units is <span class="math inline">\frac{50
-- \text{mean}}{\text{SD}} = \frac{50 - 50}{1.5} = 0</span> (no
-calculation was necessary – 0 in standard units is equal to the mean in
-original units).</li>
-<li>53 converted to standard units is <span class="math inline">\frac{53
-- \text{mean}}{\text{SD}} = \frac{53 - 50}{1.5} = 2</span>.</li>
-</ul>
-<p>Now, our problem boils down to finding the <strong>proportion of
-values in a standard normal distribution that are between 0 and
-2</strong>, or <strong>the proportion of values in a normal distribution
-that are in the interval <span class="math inline">[\text{mean},
-\text{mean} + 2 \text{ SDs}]</span></strong>.</p>
-<p>From class, we know that in a normal distribution, roughly 95% of
-values are within 2 standard deviations of the mean, i.e. the proportion
-of values in the interval <span class="math inline">[\text{mean} - 2
-\text{ SDs}, \text{mean} + 2 \text{ SDs}]</span> is 0.95.</p>
-<center><img src="../../assets/images/wi21-final/normal-solution.png" width="50%"/></center>
-<p>Since the normal distribution is symmetric about the mean, half of
-the values in this interval are to the right of the mean, and half are
-to the left. This means that the proportion of values in the interval
-<span class="math inline">[\text{mean}, \text{mean} + 2 \text{
-SDs}]</span> is <span class="math inline">\frac{0.95}{2} = 0.475</span>,
-which rounds to 0.48, and thus the desired result is 0.48.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 48%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-5">Problem 5</h2>
 <p>You need to estimate the proportion of American adults who want to be
 vaccinated against Covid-19. You plan to survey a random sample of
 American adults, and use the proportion of adults in your sample who
@@ -690,13 +613,13 @@ <h2 id="problem-5">Problem 5</h2>
 <strong>integer</strong>.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5" aria-expanded="true" aria-controls="collapse5">
+<h2 class="accordion-header" id="heading4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse4" aria-expanded="true" aria-controls="collapse4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse5" class="accordion-collapse collapse"
-aria-labelledby="heading5" data-bs-parent="#accordionExample">
+<div id="collapse4" class="accordion-collapse collapse"
+aria-labelledby="heading4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -801,6 +724,83 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <hr />
+<h2 id="problem-5">Problem 5</h2>
+<p>Suppose you draw a sample of size 100 from a population with mean 50
+and standard deviation 15. What is the probability that your sample has
+a mean between 50 and 53? Input the probability below, as a number
+between 0 and 1, rounded to <strong>two decimal places</strong>.</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse5" aria-expanded="true" aria-controls="collapse5">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse5" class="accordion-collapse collapse"
+aria-labelledby="heading5" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> 0.48</p>
+<p>This problem is testing our understanding of the Central Limit
+Theorem and normal distributions. Recall, the Central Limit Theorem
+tells us that the distribution of the sample mean is roughly normal,
+with the following characteristics:</p>
+<p><span class="math display">\begin{align*}
+\text{Mean of Distribution of Possible Sample Means} &amp;=
+\text{Population Mean} = 50 \\
+\text{SD of Distribution of Possible Sample Means} &amp;=
+\frac{\text{Population SD}}{\sqrt{\text{Sample Size}}} =
+\frac{15}{\sqrt{100}} = 1.5
+\end{align*}
+</span></p>
+<p>Given this information, it may be easier to express the problem as
+“We draw a value from a normal distribution with mean 50 and SD 1.5.
+What is the probability that the value is between 50 and 53?” Note that
+this probability is equal to the <strong>proportion of values between 50
+and 53</strong> in a normal distribution whose mean is 50 and 1.5 (since
+probabilities can be thought of as proportions).</p>
+<p>In class, we typically worked with the <em>standard</em> normal
+distribution, in which the mean was 0, the SD was 1, and the <span class="math inline">x</span>-axis represented values in standard units.
+Let’s convert the quantities of interest in this problem to standard
+units, keeping in mind that the mean and SD we’re using now are the mean
+and SD of the distribution of possible sample means, not of the
+population.</p>
+<ul>
+<li>50 converted to standard units is <span class="math inline">\frac{50
+- \text{mean}}{\text{SD}} = \frac{50 - 50}{1.5} = 0</span> (no
+calculation was necessary – 0 in standard units is equal to the mean in
+original units).</li>
+<li>53 converted to standard units is <span class="math inline">\frac{53
+- \text{mean}}{\text{SD}} = \frac{53 - 50}{1.5} = 2</span>.</li>
+</ul>
+<p>Now, our problem boils down to finding the <strong>proportion of
+values in a standard normal distribution that are between 0 and
+2</strong>, or <strong>the proportion of values in a normal distribution
+that are in the interval <span class="math inline">[\text{mean},
+\text{mean} + 2 \text{ SDs}]</span></strong>.</p>
+<p>From class, we know that in a normal distribution, roughly 95% of
+values are within 2 standard deviations of the mean, i.e. the proportion
+of values in the interval <span class="math inline">[\text{mean} - 2
+\text{ SDs}, \text{mean} + 2 \text{ SDs}]</span> is 0.95.</p>
+<center><img src="../../assets/images/wi21-final/normal-solution.png" width="50%"/></center>
+<p>Since the normal distribution is symmetric about the mean, half of
+the values in this interval are to the right of the mean, and half are
+to the left. This means that the proportion of values in the interval
+<span class="math inline">[\text{mean}, \text{mean} + 2 \text{
+SDs}]</span> is <span class="math inline">\frac{0.95}{2} = 0.475</span>,
+which rounds to 0.48, and thus the desired result is 0.48.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 48%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <p class="meta"><em>Source:</em> wi23-final — Q10</p>
 <h2 id="problem-6">Problem 6</h2>
 <p>It’s your first time playing a new game called <em>Brunch Menu</em>.
diff --git a/docs/lectures/lec19/index.html b/docs/lectures/lec19/index.html
index ce4470d..e0446ab 100644
--- a/docs/lectures/lec19/index.html
+++ b/docs/lectures/lec19/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
 </head>
 <body>
 <header id="title-block-header">
diff --git a/docs/lectures/lec2/index.html b/docs/lectures/lec2/index.html
index 00d4683..846766a 100644
--- a/docs/lectures/lec2/index.html
+++ b/docs/lectures/lec2/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
 </head>
 <body>
 <header id="title-block-header">
diff --git a/docs/lectures/lec20/index.html b/docs/lectures/lec20/index.html
index 5e16a3d..05e8090 100644
--- a/docs/lectures/lec20/index.html
+++ b/docs/lectures/lec20/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -1609,72 +1609,6 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-8">Problem 8</h2>
-<p>There are 52 IKEA locations in the United States, and there are 50
-states.</p>
-<p>Which of the following describes how to calculate the total variation
-distance between the distribution of IKEA locations by state and the
-uniform distribution?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> For each IKEA location, take the absolute difference between 1/50 and
-the number of IKEAs in the same state divided by the total number of
-IKEA locations. Sum these values across all locations and divide by
-two.</p></li>
-<li><p><input type="radio" disabled="" /> For each IKEA location, take the absolute difference between the
-number of IKEAs in the same state and the average number of IKEAs in
-each state. Sum these values across all locations and divide by two.</p></li>
-<li><p><input type="radio" disabled="" /> For each state, take the absolute difference between 1/50 and the
-number of IKEAs in that state divided by the total number of IKEA
-locations. Sum these values across all states and divide by two.</p></li>
-<li><p><input type="radio" disabled="" /> For each state, take the absolute difference between the number of
-IKEAs in that state and the average number of IKEAs in each state. Sum
-these values across all states and divide by two.</p></li>
-<li><p><input type="radio" disabled="" /> None of the above.</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading8">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8" aria-expanded="true" aria-controls="collapse8">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse8" class="accordion-collapse collapse"
-aria-labelledby="heading8" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> For each state, take the absolute
-difference between 1/50 and the number of IKEAs in that state divided by
-the total number of IKEA locations. Sum these values across all states
-and divide by two.</p>
-<p>We’re looking at the distribution across states. Since there are 50
-states, the uniform distribution would correspond to having a fraction
-of 1/50 of the IKEA locations in each state. We can picture this as a
-sequence with 50 entries that are all the same: <span class="math display">(1/50, 1/50, 1/50, 1/50, \dots)</span></p>
-<p>We want to compare this to the actual distribution of IKEAs across
-states, which we can think of as a sequence with 50 entries,
-representing the 50 states, but where each entry is the proportion of
-IKEA locations in a given state. For example, maybe the distribution
-starts out like this: <span class="math display">(3/52, 1/52, 0/52,
-1/52, \dots)</span> We can interpret each entry as the number of IKEAs
-in a state divided by the total number of IKEA locations. Note that this
-has nothing to do with the average number of IKEA locations in each
-state, which is 52/50.</p>
-<p>The way we take the TVD of two distributions is to subtract the
-distributions, take the absolute value, sum up the values, and divide by
-2. Since the entries represent states, this process aligns with the
-given answer.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 30%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-9">Problem 9</h2>
 <p>For this question, let’s think of the data in <code>app_data</code>
 as a random sample of all IKEA purchases and use it to test the
 following hypotheses.</p>
@@ -1691,7 +1625,7 @@ <h2 id="problem-9">Problem 9</h2>
 <li>2500 are in another category.</li>
 </ul>
 <p><br></p>
-<h3 id="problem-9.1">Problem 9.1</h3>
+<h3 id="problem-8.1">Problem 8.1</h3>
 <p>Which of the following <strong>could</strong> be used as the test
 statistic for this hypothesis test? Select all that apply.</p>
 <ul class="task-list">
@@ -1706,13 +1640,13 @@ <h3 id="problem-9.1">Problem 9.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_1" aria-expanded="true" aria-controls="collapse9_1">
+<h2 class="accordion-header" id="heading8_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8_1" aria-expanded="true" aria-controls="collapse8_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse9_1" class="accordion-collapse collapse"
-aria-labelledby="heading9_1" data-bs-parent="#accordionExample">
+<div id="collapse8_1" class="accordion-collapse collapse"
+aria-labelledby="heading8_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1747,7 +1681,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-9.2">Problem 9.2</h3>
+<h3 id="problem-8.2">Problem 8.2</h3>
 <p>Let’s do a hypothesis test with the following test statistic: among
 2500 beds and outdoor furniture items, the proportion of outdoor
 furniture minus the proportion of beds.</p>
@@ -1762,13 +1696,13 @@ <h3 id="problem-9.2">Problem 9.2</h3>
 <center><img src='../../assets/images/sp22-final/q8-table.jpg' width=50%></center>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_2" aria-expanded="true" aria-controls="collapse9_2">
+<h2 class="accordion-header" id="heading8_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8_2" aria-expanded="true" aria-controls="collapse8_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse9_2" class="accordion-collapse collapse"
-aria-labelledby="heading9_2" data-bs-parent="#accordionExample">
+<div id="collapse8_2" class="accordion-collapse collapse"
+aria-labelledby="heading8_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1823,7 +1757,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-9.3">Problem 9.3</h3>
+<h3 id="problem-8.3">Problem 8.3</h3>
 <p>Suppose we generate 10,000 simulated values of the test statistic
 according to the null model and store them in an array called
 <code>simulated_diffs</code>. Complete the code below to calculate the
@@ -1838,13 +1772,13 @@ <h3 id="problem-9.3">Problem 9.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_3" aria-expanded="true" aria-controls="collapse9_3">
+<h2 class="accordion-header" id="heading8_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse8_3" aria-expanded="true" aria-controls="collapse8_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse9_3" class="accordion-collapse collapse"
-aria-labelledby="heading9_3" data-bs-parent="#accordionExample">
+<div id="collapse8_3" class="accordion-collapse collapse"
+aria-labelledby="heading8_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1874,7 +1808,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-10">Problem 10</h2>
+<h2 id="problem-9">Problem 9</h2>
 <p>For this question, let’s think of the data in <code>app_data</code>
 as a random sample of all IKEA purchases and use it to test the
 following hypotheses.</p>
@@ -1891,7 +1825,7 @@ <h2 id="problem-10">Problem 10</h2>
 <li>2500 are in another category.</li>
 </ul>
 <p><br></p>
-<h3 id="problem-10.1">Problem 10.1</h3>
+<h3 id="problem-9.1">Problem 9.1</h3>
 <p>Which of the following <strong>could</strong> be used as the test
 statistic for this hypothesis test? Select all that apply.</p>
 <ul class="task-list">
@@ -1906,13 +1840,13 @@ <h3 id="problem-10.1">Problem 10.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading10_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_1" aria-expanded="true" aria-controls="collapse10_1">
+<h2 class="accordion-header" id="heading9_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_1" aria-expanded="true" aria-controls="collapse9_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10_1" class="accordion-collapse collapse"
-aria-labelledby="heading10_1" data-bs-parent="#accordionExample">
+<div id="collapse9_1" class="accordion-collapse collapse"
+aria-labelledby="heading9_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1947,7 +1881,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-10.2">Problem 10.2</h3>
+<h3 id="problem-9.2">Problem 9.2</h3>
 <p>Let’s do a hypothesis test with the following test statistic: among
 2500 beds and outdoor furniture items, the proportion of outdoor
 furniture minus the proportion of beds.</p>
@@ -1963,13 +1897,13 @@ <h3 id="problem-10.2">Problem 10.2</h3>
 <center><img src='../../assets/images/sp22-final/q8-table.jpg' width=50%></center>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading10_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_2" aria-expanded="true" aria-controls="collapse10_2">
+<h2 class="accordion-header" id="heading9_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_2" aria-expanded="true" aria-controls="collapse9_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10_2" class="accordion-collapse collapse"
-aria-labelledby="heading10_2" data-bs-parent="#accordionExample">
+<div id="collapse9_2" class="accordion-collapse collapse"
+aria-labelledby="heading9_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2024,7 +1958,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-10.3">Problem 10.3</h3>
+<h3 id="problem-9.3">Problem 9.3</h3>
 <p>Which of the following is a valid way to generate one value of the
 test statistic according to the null model? Select all that apply.</p>
 <p>Way 1:</p>
@@ -2069,13 +2003,13 @@ <h3 id="problem-10.3">Problem 10.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading10_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_3" aria-expanded="true" aria-controls="collapse10_3">
+<h2 class="accordion-header" id="heading9_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_3" aria-expanded="true" aria-controls="collapse9_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10_3" class="accordion-collapse collapse"
-aria-labelledby="heading10_3" data-bs-parent="#accordionExample">
+<div id="collapse9_3" class="accordion-collapse collapse"
+aria-labelledby="heading9_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2175,7 +2109,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-10.4">Problem 10.4</h3>
+<h3 id="problem-9.4">Problem 9.4</h3>
 <p>Suppose we generate 10,000 simulated values of the test statistic
 according to the null model and store them in an array called
 <code>simulated_diffs</code>. Complete the code below to calculate the
@@ -2191,13 +2125,13 @@ <h3 id="problem-10.4">Problem 10.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading10_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_4" aria-expanded="true" aria-controls="collapse10_4">
+<h2 class="accordion-header" id="heading9_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_4" aria-expanded="true" aria-controls="collapse9_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10_4" class="accordion-collapse collapse"
-aria-labelledby="heading10_4" data-bs-parent="#accordionExample">
+<div id="collapse9_4" class="accordion-collapse collapse"
+aria-labelledby="heading9_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2227,6 +2161,72 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-10">Problem 10</h2>
+<p>There are 52 IKEA locations in the United States, and there are 50
+states.</p>
+<p>Which of the following describes how to calculate the total variation
+distance between the distribution of IKEA locations by state and the
+uniform distribution?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> For each IKEA location, take the absolute difference between 1/50 and
+the number of IKEAs in the same state divided by the total number of
+IKEA locations. Sum these values across all locations and divide by
+two.</p></li>
+<li><p><input type="radio" disabled="" /> For each IKEA location, take the absolute difference between the
+number of IKEAs in the same state and the average number of IKEAs in
+each state. Sum these values across all locations and divide by two.</p></li>
+<li><p><input type="radio" disabled="" /> For each state, take the absolute difference between 1/50 and the
+number of IKEAs in that state divided by the total number of IKEA
+locations. Sum these values across all states and divide by two.</p></li>
+<li><p><input type="radio" disabled="" /> For each state, take the absolute difference between the number of
+IKEAs in that state and the average number of IKEAs in each state. Sum
+these values across all states and divide by two.</p></li>
+<li><p><input type="radio" disabled="" /> None of the above.</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading10">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10" aria-expanded="true" aria-controls="collapse10">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse10" class="accordion-collapse collapse"
+aria-labelledby="heading10" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> For each state, take the absolute
+difference between 1/50 and the number of IKEAs in that state divided by
+the total number of IKEA locations. Sum these values across all states
+and divide by two.</p>
+<p>We’re looking at the distribution across states. Since there are 50
+states, the uniform distribution would correspond to having a fraction
+of 1/50 of the IKEA locations in each state. We can picture this as a
+sequence with 50 entries that are all the same: <span class="math display">(1/50, 1/50, 1/50, 1/50, \dots)</span></p>
+<p>We want to compare this to the actual distribution of IKEAs across
+states, which we can think of as a sequence with 50 entries,
+representing the 50 states, but where each entry is the proportion of
+IKEA locations in a given state. For example, maybe the distribution
+starts out like this: <span class="math display">(3/52, 1/52, 0/52,
+1/52, \dots)</span> We can interpret each entry as the number of IKEAs
+in a state divided by the total number of IKEA locations. Note that this
+has nothing to do with the average number of IKEA locations in each
+state, which is 52/50.</p>
+<p>The way we take the TVD of two distributions is to subtract the
+distributions, take the absolute value, sum up the values, and divide by
+2. Since the entries represent states, this process aligns with the
+given answer.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 30%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <p class="meta"><em>Source:</em> sp23-final — Q5</p>
 <h2 id="problem-11">Problem 11</h2>
 <p>In some cities, the number of sunshine hours per month is relatively
@@ -3105,8 +3105,10 @@ <h2 class="accordion-header" id="heading14_2">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer</strong>:</p>
-<p><code>(a): np.random.permutation(tributes.get("Days))</code></p>
-<p><code>(b): means.loc[True] - means.loc[False]</code></p>
+<p><code>(a)</code>:
+<code>Days = np.random.permutation(tributes.get("Days))</code> OR
+<code>Career = np.random.permutation(tributes.get("Career))</code></p>
+<p><code>(b)</code>: <code>means.loc[True] - means.loc[False]</code></p>
 <p>In blank a we shuffle one of the columns so as to break any real link
 between the Career column and the Days column. This allows us to
 simulate our null hypothesis. After this in blank b, we use
@@ -4034,7 +4036,8 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <h3 id="problem-17.4">Problem 17.4</h3>
 <p>Below, we present the same code that is given at the start of the
-problem.</p>
+problem. (Remember to keep the data description from the top of the exam
+open in another tab!)</p>
 <div class="sourceCode" id="cb37"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
 <span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(<span class="dv">10000</span>):</span>
@@ -4499,8 +4502,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <h3 id="problem-18.4">Problem 18.4</h3>
 <p>Below, we present the same code that is given at the start of the
-problem. (Remember to keep the data description from the top of the exam
-open in another tab!)</p>
+problem.</p>
 <div class="sourceCode" id="cb49"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
 <span id="cb49-2"><a href="#cb49-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(<span class="dv">10000</span>):</span>
diff --git a/docs/lectures/lec21/index.html b/docs/lectures/lec21/index.html
index 8ca76b0..6187df0 100644
--- a/docs/lectures/lec21/index.html
+++ b/docs/lectures/lec21/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/lectures/lec22/index.html b/docs/lectures/lec22/index.html
index 9c7abf1..ceb17da 100644
--- a/docs/lectures/lec22/index.html
+++ b/docs/lectures/lec22/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -138,14 +138,8 @@ <h1 id="lecture-22-collected-practice-questions">Lecture 22 — Collected
 (rendered directly from the original exam/quiz sources).</p>
 <hr />
 <h2 id="problem-1">Problem 1</h2>
-<p>Researchers from the San Diego Zoo, located within Balboa Park,
-collected physical measurements of three species of penguins (Adelie,
-Chinstrap, or Gentoo) in a region of Antarctica. One piece of
-information they tracked for each of 330 penguins was its mass in grams.
-The average penguin mass is 4200 grams, and the standard deviation is
-840 grams.</p>
-<p>We’re interested in investigating the differences between the masses
-of Adelie penguins and Chinstrap penguins. Specifically, our null
+<p>We’re now interested in investigating the differences between the
+masses of Adelie penguins and Chinstrap penguins. Specifically, our null
 hypothesis is that their masses are drawn from the same population
 distribution, and any observed differences are due to chance only.</p>
 <p>Below, we have a snippet of working code for this hypothesis test,
@@ -317,29 +311,9 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-1.4">Problem 1.4</h3>
-<p>For your convenience, we copy the code for the hypothesis test
-below.</p>
-<div class="sourceCode" id="cb4"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
-<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
-<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
-<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
-<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
-<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
-<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
-<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
-<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
-<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
-<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
-<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
-<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
-<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we removed <code>line (a)</code>, and replaced
 <code>line (b)</code> with</p>
-<div class="sourceCode" id="cb5"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb4"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)</span></code></pre></div>
 <p>Select the best answer.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> This would still run a valid hypothesis test</p></li>
@@ -385,29 +359,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-1.5">Problem 1.5</h3>
-<p>For your convenience, we copy the code for the hypothesis test
-below.</p>
-<div class="sourceCode" id="cb6"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
-<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
-<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
-<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
-<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
-<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
-<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
-<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
-<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
-<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
-<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
-<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
-<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
-<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we removed <code>line (a)</code>, and replaced
 <code>line (b)</code> with</p>
-<div class="sourceCode" id="cb7"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb5"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
 <p>Select the best answer.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> This would still run a valid hypothesis test</p></li>
@@ -454,35 +408,14 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-1.6">Problem 1.6</h3>
-<p>For your convenience, we copy the code for the hypothesis test
-below.</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
-<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
-<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
-<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
-<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
-<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
-<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
-<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
-<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
-<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
-<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
-<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
-<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
-<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-18"><a href="#cb8-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we replaced <code>line (a)</code> with</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.assign(</span>
-<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>    species<span class="op">=</span>np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>)</span>
-<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
+<div class="sourceCode" id="cb6"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.assign(</span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>    species<span class="op">=</span>np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>)</span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
 <p>and replaced line (b) with</p>
-<div class="sourceCode" id="cb10"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> with_shuffled.assign(</span>
-<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>    mass<span class="op">=</span>np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;mass&#39;</span>)</span>
-<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
+<div class="sourceCode" id="cb7"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> with_shuffled.assign(</span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>    mass<span class="op">=</span>np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;mass&#39;</span>)</span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
 <p>Select the best answer.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> This would still run a valid hypothesis test</p></li>
@@ -527,6 +460,7 @@ <h3 id="problem-1.7">Problem 1.7</h3>
 empirical distribution for the test statistic. In red is the observed
 statistic.</p>
 <center><img src='../../assets/images/fa21-final/measuring_up_his.png' width=40%></center>
+<p><br></p>
 <p>Suppose our alternative hypothesis is that Chinstrap penguins weigh
 more on average than Adelie penguins. Which of the following is closest
 to the p-value for our hypothesis test?</p>
@@ -576,33 +510,38 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-2">Problem 2</h2>
-<p>We’re now interested in investigating the differences between the
-masses of Adelie penguins and Chinstrap penguins. Specifically, our null
+<p>Researchers from the San Diego Zoo, located within Balboa Park,
+collected physical measurements of three species of penguins (Adelie,
+Chinstrap, or Gentoo) in a region of Antarctica. One piece of
+information they tracked for each of 330 penguins was its mass in grams.
+The average penguin mass is 4200 grams, and the standard deviation is
+840 grams.</p>
+<p>We’re interested in investigating the differences between the masses
+of Adelie penguins and Chinstrap penguins. Specifically, our null
 hypothesis is that their masses are drawn from the same population
 distribution, and any observed differences are due to chance only.</p>
 <p>Below, we have a snippet of working code for this hypothesis test,
 for a specific test statistic. Assume that <code>adelie_chinstrap</code>
 is a DataFrame of only Adelie and Chinstrap penguins, with just two
 columns – <code>'species'</code> and <code>'mass'</code>.</p>
-<div class="sourceCode" id="cb11"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
-<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
-<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
-<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
-<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
-<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
-<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
-<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
-<span id="cb11-10"><a href="#cb11-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
-<span id="cb11-11"><a href="#cb11-11" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb11-12"><a href="#cb11-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
-<span id="cb11-13"><a href="#cb11-13" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb11-14"><a href="#cb11-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
-<span id="cb11-15"><a href="#cb11-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
-<span id="cb11-16"><a href="#cb11-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
-<span id="cb11-17"><a href="#cb11-17" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb11-18"><a href="#cb11-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
+<div class="sourceCode" id="cb8"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
+<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
+<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
+<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>    </span>
+<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
+<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
+<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
+<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
+<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
+<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
+<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
+<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb8-18"><a href="#cb8-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p><br></p>
 <h3 id="problem-2.1">Problem 2.1</h3>
 <p>Which of the following statements best describe the procedure
@@ -665,11 +604,10 @@ <h3 id="problem-2.2">Problem 2.2</h3>
 following options compute the exact same statistic as line (c) currently
 does?</p>
 <p>Option 1:</p>
-<div class="sourceCode" id="cb12"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Adelie&#39;</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Chinstrap&#39;</span>]</span></code></pre></div>
+<div class="sourceCode" id="cb9"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Adelie&#39;</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Chinstrap&#39;</span>]</span></code></pre></div>
 <p>Option 2:</p>
-<div class="sourceCode" id="cb13"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Chinstrap&#39;</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Adelie&#39;</span>]</span></code></pre></div>
+<div class="sourceCode" id="cb10"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Chinstrap&#39;</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).loc[<span class="st">&#39;Adelie&#39;</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> Option 1 only</p></li>
 <li><p><input type="radio" disabled="" /> Option 2 only</p></li>
@@ -752,10 +690,31 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-2.4">Problem 2.4</h3>
+<p>For your convenience, we copy the code for the hypothesis test
+below.</p>
+<div class="sourceCode" id="cb11"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
+<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
+<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
+<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
+<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
+<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>    </span>
+<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
+<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
+<span id="cb11-10"><a href="#cb11-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
+<span id="cb11-11"><a href="#cb11-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb11-12"><a href="#cb11-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
+<span id="cb11-13"><a href="#cb11-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb11-14"><a href="#cb11-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
+<span id="cb11-15"><a href="#cb11-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
+<span id="cb11-16"><a href="#cb11-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
+<span id="cb11-17"><a href="#cb11-17" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb11-18"><a href="#cb11-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we removed <code>line (a)</code>, and replaced
 <code>line (b)</code> with</p>
-<div class="sourceCode" id="cb14"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb12"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">False</span>)</span></code></pre></div>
 <p>Select the best answer.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> This would still run a valid hypothesis test</p></li>
@@ -801,10 +760,31 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-2.5">Problem 2.5</h3>
+<p>For your convenience, we copy the code for the hypothesis test
+below.</p>
+<div class="sourceCode" id="cb13"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
+<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
+<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
+<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
+<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
+<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
+<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a>    </span>
+<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
+<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
+<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
+<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
+<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
+<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
+<span id="cb13-16"><a href="#cb13-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
+<span id="cb13-17"><a href="#cb13-17" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb13-18"><a href="#cb13-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we removed <code>line (a)</code>, and replaced
 <code>line (b)</code> with</p>
-<div class="sourceCode" id="cb15"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb14"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.sample(adelie_chinstrap.shape[<span class="dv">0</span>], replace<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
 <p>Select the best answer.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> This would still run a valid hypothesis test</p></li>
@@ -851,6 +831,27 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <h3 id="problem-2.6">Problem 2.6</h3>
+<p>For your convenience, we copy the code for the hypothesis test
+below.</p>
+<div class="sourceCode" id="cb15"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>stats <span class="op">=</span> np.array([])</span>
+<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>num_reps <span class="op">=</span> <span class="dv">500</span></span>
+<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> i <span class="kw">in</span> np.arange(num_reps):</span>
+<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) starts ---</span></span>
+<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a>    shuffled <span class="op">=</span> np.random.permutation(adelie_chinstrap.get(<span class="st">&#39;species&#39;</span>))</span>
+<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (a) ends ---</span></span>
+<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a>    </span>
+<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) starts ---</span></span>
+<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a>    with_shuffled <span class="op">=</span> adelie_chinstrap.assign(species<span class="op">=</span>shuffled)</span>
+<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (b) ends ---</span></span>
+<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> with_shuffled.groupby(<span class="st">&#39;species&#39;</span>).mean()</span>
+<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) starts ---</span></span>
+<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a>    stat <span class="op">=</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">0</span>] <span class="op">-</span> grouped.get(<span class="st">&#39;mass&#39;</span>).iloc[<span class="dv">1</span>]</span>
+<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a>    <span class="co"># --- line (c) ends ---</span></span>
+<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a>    stats <span class="op">=</span> np.append(stats, stat)</span></code></pre></div>
 <p>What would happen if we replaced <code>line (a)</code> with</p>
 <div class="sourceCode" id="cb16"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>with_shuffled <span class="op">=</span> adelie_chinstrap.assign(</span>
@@ -905,7 +906,6 @@ <h3 id="problem-2.7">Problem 2.7</h3>
 empirical distribution for the test statistic. In red is the observed
 statistic.</p>
 <center><img src='../../assets/images/fa21-final/measuring_up_his.png' width=40%></center>
-<p><br></p>
 <p>Suppose our alternative hypothesis is that Chinstrap penguins weigh
 more on average than Adelie penguins. Which of the following is closest
 to the p-value for our hypothesis test?</p>
@@ -2632,8 +2632,7 @@ <h2 id="problem-9">Problem 9</h2>
 <p>Answer the following true/false questions.</p>
 <p><br></p>
 <h3 id="problem-9.1">Problem 9.1</h3>
-<p>For a given sample, a 90% confidence interval is narrower than a 95%
-confidence interval.</p>
+<p><code>df.groupby("kind").mean()</code> will have 5 columns.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> True</p></li>
 <li><p><input type="radio" disabled="" /> False</p></li>
@@ -2652,122 +2651,123 @@ <h2 class="accordion-header" id="heading9_1">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer: </strong> True</p>
-<p>The more narrow an interval is, the less confident one is that the
-intervals one creates will contain the true population parameter.</p>
+<p>Referring to <code>df</code> at the beginning of the exam, we could
+see that 5 of the columns have numerical values as inputs, and thus
+<code>df.groupby("kind").mean()</code> will return the mean of these 5
+numerical columns</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 74%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
+<hr />
+<h2 id="problem-10">Problem 10</h2>
+<p>Answer the following true/false questions.</p>
 <p><br></p>
-<h3 id="problem-9.2">Problem 9.2</h3>
-<p>The distribution of sample proportions is roughly normal for large
-samples because of the Central Limit Theorem.</p>
+<h3 id="problem-10.1">Problem 10.1</h3>
+<p>For a given sample, a 90% confidence interval is narrower than a 95%
+confidence interval.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> True</p></li>
 <li><p><input type="radio" disabled="" /> False</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_2" aria-expanded="true" aria-controls="collapse9_2">
+<h2 class="accordion-header" id="heading10_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_1" aria-expanded="true" aria-controls="collapse10_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse9_2" class="accordion-collapse collapse"
-aria-labelledby="heading9_2" data-bs-parent="#accordionExample">
+<div id="collapse10_1" class="accordion-collapse collapse"
+aria-labelledby="heading10_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer: </strong> True</p>
-<p>This is just the definition of Central Limit Theorem. Remember that a
-proportion is a mean of 0s and 1s.</p>
+<p>The more narrow an interval is, the less confident one is that the
+intervals one creates will contain the true population parameter.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 43%.</p>
+<p>The average score on this problem was 91%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <p><br></p>
-<h3 id="problem-9.3">Problem 9.3</h3>
-<p>Chebyshev’s inequality implies that we can always create at least a
-96% confidence interval from a bootstrap distribution using the mean of
-the distribution plus or minus 5 standard deviations.</p>
+<h3 id="problem-10.2">Problem 10.2</h3>
+<p>The distribution of sample proportions is roughly normal for large
+samples because of the Central Limit Theorem.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> True</p></li>
 <li><p><input type="radio" disabled="" /> False</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_3" aria-expanded="true" aria-controls="collapse9_3">
+<h2 class="accordion-header" id="heading10_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_2" aria-expanded="true" aria-controls="collapse10_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse9_3" class="accordion-collapse collapse"
-aria-labelledby="heading9_3" data-bs-parent="#accordionExample">
+<div id="collapse10_2" class="accordion-collapse collapse"
+aria-labelledby="heading10_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer: </strong> True</p>
-<p>By Chebyshev’s theorem, at least <code>1 - 1 / z^2</code> of the data
-is within <code>z</code> STD of the mean. Thus
-<code>1 - 1 / 5^2 = 0.96</code> of the data is within 5 STD of the
-mean.</p>
+<p>This is just the definition of Central Limit Theorem. Remember that a
+proportion is a mean of 0s and 1s.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 51%.</p>
+<p>The average score on this problem was 43%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<hr />
-<h2 id="problem-10">Problem 10</h2>
-<p>Answer the following true/false questions.</p>
 <p><br></p>
-<h3 id="problem-10.1">Problem 10.1</h3>
-<p><code>df.groupby("kind").mean()</code> will have 5 columns.</p>
+<h3 id="problem-10.3">Problem 10.3</h3>
+<p>Chebyshev’s inequality implies that we can always create at least a
+96% confidence interval from a bootstrap distribution using the mean of
+the distribution plus or minus 5 standard deviations.</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> True</p></li>
 <li><p><input type="radio" disabled="" /> False</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading10_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_1" aria-expanded="true" aria-controls="collapse10_1">
+<h2 class="accordion-header" id="heading10_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_3" aria-expanded="true" aria-controls="collapse10_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10_1" class="accordion-collapse collapse"
-aria-labelledby="heading10_1" data-bs-parent="#accordionExample">
+<div id="collapse10_3" class="accordion-collapse collapse"
+aria-labelledby="heading10_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer: </strong> True</p>
-<p>Referring to <code>df</code> at the beginning of the exam, we could
-see that 5 of the columns have numerical values as inputs, and thus
-<code>df.groupby("kind").mean()</code> will return the mean of these 5
-numerical columns</p>
+<p>By Chebyshev’s theorem, at least <code>1 - 1 / z^2</code> of the data
+is within <code>z</code> STD of the mean. Thus
+<code>1 - 1 / 5^2 = 0.96</code> of the data is within 5 STD of the
+mean.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 74%.</p>
+<p>The average score on this problem was 51%.</p>
 </div>
 </div>
 </div>
@@ -2775,17 +2775,16 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-11">Problem 11</h2>
-<p>Answer the following true/false questions.</p>
+<p>Suppose Tiffany has a random sample of dogs. Select the most
+appropriate technique to answer each of the following questions using
+Tiffany’s dog sample.</p>
 <p><br></p>
 <h3 id="problem-11.1">Problem 11.1</h3>
-<p><span style="color:red"><b>Note: This problem is out of scope; it
-covers material no longer included in the course.</b></span></p>
-<p>When John Snow took off the handle from the Broad Street pump, the
-number of cholera deaths decreased. Because of this, he could conclude
-that cholera was caused by dirty water.</p>
+<p>Do small dogs typically live longer than medium and large dogs?</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
+<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
+<li><p><input type="radio" disabled="" /> Permutation test</p></li>
+<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
@@ -2800,30 +2799,32 @@ <h2 class="accordion-header" id="heading11_1">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> False</p>
-<p>There are a couple details that the problem fails to convey and that
-we cannot assume. 1) Do we even know that the pump he removed was the
-only pump with dirty water? 2) Do we know that people even drank/took
-water from the Broad Street pump? 3) Do we even know what kinds of
-people drank from the Broad Street pump? We need to eliminate all
-confounding factors, otherwise, it might be difficult to identify
-causality.</p>
+<p><strong>Answer: </strong> Option 2: Permutation test.</p>
+<p>We have two parameters: dog size and life expectancy. Here if there
+was no significant statistical difference between the life expectancy of
+different dog sizes, randomly assigning our sampled life expectancy to
+each dog should lead us to observe similar observations to the observed
+statistic. Thus using a permutation test to comapre the two groups makes
+the most sense. We’re not really trying to estimate a spcecific value so
+bootstrapping isn’t a good idea here. Also, there’s not really a good
+way to randomly generate life expectancies so a hypothesis test is not a
+good idea here.</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 77%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-11.2">Problem 11.2</h3>
-<p>If you get a p-value of 0.009 using a permutation test, you can
-conclude causality.</p>
+<p>Does Tiffany’s sample have an even distribution of dog kinds?</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
+<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
+<li><p><input type="radio" disabled="" /> Permutation test</p></li>
+<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
@@ -2838,25 +2839,29 @@ <h2 class="accordion-header" id="heading11_2">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> False</p>
-<p>Permutation tests don’t prove causality. Remember, we use the
-permutation test and calculate a p-value to simply reject a null
-hypothesis, not to prove the alternative hypothesis.</p>
+<p><strong>Answer: </strong> Option 1: Standard hypothesis test.</p>
+<p>We’re not really comparing a variable between two groups, but rather
+looking at the overall distribution, so Permutation testing wouldn’t
+work too well here. Again, we’re not really trying to estimate anything
+here so bootstrapping isn’t a good idea. This leaves us with the
+Standard Hypothesis Test, which makes sense if we use Total Variation
+Distance as our test statistic.</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 51%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-11.3">Problem 11.3</h3>
-<p><code>df.groupby("kind").mean()</code> will have 5 columns.</p>
+<p>What’s the median weight for herding dogs?</p>
 <ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
+<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
+<li><p><input type="radio" disabled="" /> Permutation test</p></li>
+<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
@@ -2871,7 +2876,155 @@ <h2 class="accordion-header" id="heading11_3">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> True</p>
+<p><strong>Answer: </strong> Option 3: Bootstrapping</p>
+<p>Here we’re trying to determine a specific value, which immediately
+leads us to bootstrapping. The other two tests wouldn’t really make
+sense in this context.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 83%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-11.4">Problem 11.4</h3>
+<p>Do dogs live longer than 12 years on average?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
+<li><p><input type="radio" disabled="" /> Permutation test</p></li>
+<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading11_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_4" aria-expanded="true" aria-controls="collapse11_4">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse11_4" class="accordion-collapse collapse"
+aria-labelledby="heading11_4" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> Option 3: Bootstrapping</p>
+<p>While the wording here might throw us off, we’re really just trying
+to determine the average life expectancy of dogs, and then see how that
+compares to 12. This leads us to bootstrapping since we’re trying to
+determine a specific value. The other two tests wouldn’t really make
+sense in this context.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 43%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-12">Problem 12</h2>
+<p>Answer the following true/false questions.</p>
+<p><br></p>
+<h3 id="problem-12.1">Problem 12.1</h3>
+<p><span style="color:red"><b>Note: This problem is out of scope; it
+covers material no longer included in the course.</b></span></p>
+<p>When John Snow took off the handle from the Broad Street pump, the
+number of cholera deaths decreased. Because of this, he could conclude
+that cholera was caused by dirty water.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading12_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_1" aria-expanded="true" aria-controls="collapse12_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse12_1" class="accordion-collapse collapse"
+aria-labelledby="heading12_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> False</p>
+<p>There are a couple details that the problem fails to convey and that
+we cannot assume. 1) Do we even know that the pump he removed was the
+only pump with dirty water? 2) Do we know that people even drank/took
+water from the Broad Street pump? 3) Do we even know what kinds of
+people drank from the Broad Street pump? We need to eliminate all
+confounding factors, otherwise, it might be difficult to identify
+causality.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 91%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-12.2">Problem 12.2</h3>
+<p>If you get a p-value of 0.009 using a permutation test, you can
+conclude causality.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading12_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_2" aria-expanded="true" aria-controls="collapse12_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse12_2" class="accordion-collapse collapse"
+aria-labelledby="heading12_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> False</p>
+<p>Permutation tests don’t prove causality. Remember, we use the
+permutation test and calculate a p-value to simply reject a null
+hypothesis, not to prove the alternative hypothesis.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 91%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-12.3">Problem 12.3</h3>
+<p><code>df.groupby("kind").mean()</code> will have 5 columns.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading12_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_3" aria-expanded="true" aria-controls="collapse12_3">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse12_3" class="accordion-collapse collapse"
+aria-labelledby="heading12_3" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> True</p>
 <p>Referring to <code>df</code> at the beginning of the exam, we could
 see that 5 of the columns have numerical values as inputs, and thus
 <code>df.groupby("kind").mean()</code> will return the mean of these 5
@@ -2886,18 +3039,18 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.4">Problem 11.4</h3>
+<h3 id="problem-12.4">Problem 12.4</h3>
 <p>If the 95% confidence interval for dog price is [650, 900], there is
 a 95% chance that the population dog price is between $650 and $900.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_4" aria-expanded="true" aria-controls="collapse11_4">
+<h2 class="accordion-header" id="heading12_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_4" aria-expanded="true" aria-controls="collapse12_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_4" class="accordion-collapse collapse"
-aria-labelledby="heading11_4" data-bs-parent="#accordionExample">
+<div id="collapse12_4" class="accordion-collapse collapse"
+aria-labelledby="heading12_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2920,7 +3073,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.5">Problem 11.5</h3>
+<h3 id="problem-12.5">Problem 12.5</h3>
 <p>For a given sample, an 90% confidence interval is narrower than a 95%
 confidence interval.</p>
 <ul class="task-list">
@@ -2929,13 +3082,13 @@ <h3 id="problem-11.5">Problem 11.5</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_5" aria-expanded="true" aria-controls="collapse11_5">
+<h2 class="accordion-header" id="heading12_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_5" aria-expanded="true" aria-controls="collapse12_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_5" class="accordion-collapse collapse"
-aria-labelledby="heading11_5" data-bs-parent="#accordionExample">
+<div id="collapse12_5" class="accordion-collapse collapse"
+aria-labelledby="heading12_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2953,7 +3106,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.6">Problem 11.6</h3>
+<h3 id="problem-12.6">Problem 12.6</h3>
 <p>If you tried to bootstrap your sample 1,000 times but accidentally
 sampled <strong>without</strong> replacement, the standard deviation of
 your test statistics is always equal to 0.</p>
@@ -2963,13 +3116,13 @@ <h3 id="problem-11.6">Problem 11.6</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_6">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_6" aria-expanded="true" aria-controls="collapse11_6">
+<h2 class="accordion-header" id="heading12_6">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_6" aria-expanded="true" aria-controls="collapse12_6">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_6" class="accordion-collapse collapse"
-aria-labelledby="heading11_6" data-bs-parent="#accordionExample">
+<div id="collapse12_6" class="accordion-collapse collapse"
+aria-labelledby="heading12_6" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2989,7 +3142,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.7">Problem 11.7</h3>
+<h3 id="problem-12.7">Problem 12.7</h3>
 <p>You run a permutation test and store 500 simulated test statistics in
 an array called <code>stats</code>. You can construct a 95% confidence
 interval by finding the 2.5th and 97.5th percentiles of
@@ -3000,13 +3153,13 @@ <h3 id="problem-11.7">Problem 11.7</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_7">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_7" aria-expanded="true" aria-controls="collapse11_7">
+<h2 class="accordion-header" id="heading12_7">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_7" aria-expanded="true" aria-controls="collapse12_7">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_7" class="accordion-collapse collapse"
-aria-labelledby="heading11_7" data-bs-parent="#accordionExample">
+<div id="collapse12_7" class="accordion-collapse collapse"
+aria-labelledby="heading12_7" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3024,7 +3177,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.8">Problem 11.8</h3>
+<h3 id="problem-12.8">Problem 12.8</h3>
 <p>The distribution of sample proportions is roughly normal for large
 samples because of the Central Limit Theorem.</p>
 <ul class="task-list">
@@ -3033,13 +3186,13 @@ <h3 id="problem-11.8">Problem 11.8</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_8">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_8" aria-expanded="true" aria-controls="collapse11_8">
+<h2 class="accordion-header" id="heading12_8">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_8" aria-expanded="true" aria-controls="collapse12_8">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_8" class="accordion-collapse collapse"
-aria-labelledby="heading11_8" data-bs-parent="#accordionExample">
+<div id="collapse12_8" class="accordion-collapse collapse"
+aria-labelledby="heading12_8" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3056,7 +3209,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.9">Problem 11.9</h3>
+<h3 id="problem-12.9">Problem 12.9</h3>
 <p><span style="color:red"><b>Note: This problem is out of scope; it
 covers material no longer included in the course.</b></span></p>
 <p>The 20th percentile of the sequence [10, 30, 50, 40, 9, 70] is
@@ -3067,13 +3220,13 @@ <h3 id="problem-11.9">Problem 11.9</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_9">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_9" aria-expanded="true" aria-controls="collapse11_9">
+<h2 class="accordion-header" id="heading12_9">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_9" aria-expanded="true" aria-controls="collapse12_9">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_9" class="accordion-collapse collapse"
-aria-labelledby="heading11_9" data-bs-parent="#accordionExample">
+<div id="collapse12_9" class="accordion-collapse collapse"
+aria-labelledby="heading12_9" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3103,19 +3256,19 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.10">Problem 11.10</h3>
+<h3 id="problem-12.10">Problem 12.10</h3>
 <p>Chebyshev’s inequality implies that we can always create a 96%
 confidence interval from a bootstrap distribution using the mean of the
 distribution plus or minus 5 standard deviations.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_10">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_10" aria-expanded="true" aria-controls="collapse11_10">
+<h2 class="accordion-header" id="heading12_10">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_10" aria-expanded="true" aria-controls="collapse12_10">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_10" class="accordion-collapse collapse"
-aria-labelledby="heading11_10" data-bs-parent="#accordionExample">
+<div id="collapse12_10" class="accordion-collapse collapse"
+aria-labelledby="heading12_10" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3136,159 +3289,6 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-12">Problem 12</h2>
-<p>Suppose Tiffany has a random sample of dogs. Select the most
-appropriate technique to answer each of the following questions using
-Tiffany’s dog sample.</p>
-<p><br></p>
-<h3 id="problem-12.1">Problem 12.1</h3>
-<p>Do small dogs typically live longer than medium and large dogs?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
-<li><p><input type="radio" disabled="" /> Permutation test</p></li>
-<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading12_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_1" aria-expanded="true" aria-controls="collapse12_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse12_1" class="accordion-collapse collapse"
-aria-labelledby="heading12_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> Option 2: Permutation test.</p>
-<p>We have two parameters: dog size and life expectancy. Here if there
-was no significant statistical difference between the life expectancy of
-different dog sizes, randomly assigning our sampled life expectancy to
-each dog should lead us to observe similar observations to the observed
-statistic. Thus using a permutation test to comapre the two groups makes
-the most sense. We’re not really trying to estimate a spcecific value so
-bootstrapping isn’t a good idea here. Also, there’s not really a good
-way to randomly generate life expectancies so a hypothesis test is not a
-good idea here.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 77%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-12.2">Problem 12.2</h3>
-<p>Does Tiffany’s sample have an even distribution of dog kinds?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
-<li><p><input type="radio" disabled="" /> Permutation test</p></li>
-<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading12_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_2" aria-expanded="true" aria-controls="collapse12_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse12_2" class="accordion-collapse collapse"
-aria-labelledby="heading12_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> Option 1: Standard hypothesis test.</p>
-<p>We’re not really comparing a variable between two groups, but rather
-looking at the overall distribution, so Permutation testing wouldn’t
-work too well here. Again, we’re not really trying to estimate anything
-here so bootstrapping isn’t a good idea. This leaves us with the
-Standard Hypothesis Test, which makes sense if we use Total Variation
-Distance as our test statistic.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 51%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-12.3">Problem 12.3</h3>
-<p>What’s the median weight for herding dogs?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
-<li><p><input type="radio" disabled="" /> Permutation test</p></li>
-<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading12_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_3" aria-expanded="true" aria-controls="collapse12_3">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse12_3" class="accordion-collapse collapse"
-aria-labelledby="heading12_3" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> Option 3: Bootstrapping</p>
-<p>Here we’re trying to determine a specific value, which immediately
-leads us to bootstrapping. The other two tests wouldn’t really make
-sense in this context.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 83%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-12.4">Problem 12.4</h3>
-<p>Do dogs live longer than 12 years on average?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> Standard hypothesis test</p></li>
-<li><p><input type="radio" disabled="" /> Permutation test</p></li>
-<li><p><input type="radio" disabled="" /> Bootstrapping</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading12_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_4" aria-expanded="true" aria-controls="collapse12_4">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse12_4" class="accordion-collapse collapse"
-aria-labelledby="heading12_4" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> Option 3: Bootstrapping</p>
-<p>While the wording here might throw us off, we’re really just trying
-to determine the average life expectancy of dogs, and then see how that
-compares to 12. This leads us to bootstrapping since we’re trying to
-determine a specific value. The other two tests wouldn’t really make
-sense in this context.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 43%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
 <p class="meta"><em>Source:</em> su24-final — Q6</p>
 <h2 id="problem-13">Problem 13</h2>
 <p>You want to use the data in <code>stages</code> to test the following
@@ -3823,10 +3823,59 @@ <h2 id="problem-16">Problem 16</h2>
 <p><br></p>
 <h3 id="problem-16.1">Problem 16.1</h3>
 <p>It turns out that Kelsey Plum averages 0.61 more assists in games
-that she wins than in games that she loses. After observing that Kelsey
-Plum averages more assists in winning games than in losing games, we
-become interested in conducting a permutation test for the following
-hypotheses:</p>
+that she wins (“winning games”) than in games that she loses (“losing
+games”). Fill in the blanks below so that <code>observed_diff</code>
+evaluates to -0.61.</p>
+<div class="sourceCode" id="cb30"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>observed_diff <span class="op">=</span> diff_in_group_means(plum, __(a)__, __(b)__)</span></code></pre></div>
+<ol type="1">
+<li><p>What goes in blank (a)?</p></li>
+<li><p>What goes in blank (b)?</p></li>
+</ol>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading16_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_1" aria-expanded="true" aria-controls="collapse16_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse16_1" class="accordion-collapse collapse"
+aria-labelledby="heading16_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answers:</strong> <code>'Won'</code>, <code>'AST'</code></p>
+<p>To compute the number of assists Kelsey Plum averages in winning and
+losing games, we need to group by <code>'Won'</code>. Once doing so, and
+using the <code>.mean()</code> aggregation method, we need to access
+elements in the <code>'AST'</code> column.</p>
+<p>The second argument to <code>diff_in_group_means</code>,
+<code>group_col</code>, is the column we’re grouping by, and so blank
+(a) must be filled by <code>'Won'</code>. Then, the second argument,
+<code>num_col</code>, must be <code>'AST'</code>.</p>
+<p>Note that after extracting the Series containing the average number
+of assists in wins and losses, we are returning the value with the index
+<code>False</code> (“loss”) minus the value with the index
+<code>True</code> (“win”). So, throughout this problem, keep in mind
+that we are computing “losses minus wins”. Since our observation was
+that she averaged 0.61 more assists in wins than in losses, it makes
+sense that <code>diff_in_group_means(plum, 'Won', 'AST')</code> is -0.61
+(rather than +0.61).</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 94%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-16.2">Problem 16.2</h3>
+<p>After observing that Kelsey Plum averages more assists in winning
+games than in losing games, we become interested in conducting a
+permutation test for the following hypotheses:</p>
 <ul>
 <li><strong>Null Hypothesis:</strong> The number of assists Kelsey Plum
 makes in winning games and in losing games come from the same
@@ -3837,12 +3886,12 @@ <h3 id="problem-16.1">Problem 16.1</h3>
 </ul>
 <p>To conduct our permutation test, we place the following code in a
 <code>for</code>-loop.</p>
-<div class="sourceCode" id="cb30"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>won <span class="op">=</span> plum.get(<span class="st">&#39;Won&#39;</span>)</span>
-<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>ast <span class="op">=</span> plum.get(<span class="st">&#39;AST&#39;</span>)</span>
-<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>shuffled <span class="op">=</span> plum.assign(Won_shuffled<span class="op">=</span>np.random.permutation(won)) <span class="op">\</span></span>
-<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>               .assign(AST_shuffled<span class="op">=</span>np.random.permutation(ast))</span></code></pre></div>
+<div class="sourceCode" id="cb31"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>won <span class="op">=</span> plum.get(<span class="st">&#39;Won&#39;</span>)</span>
+<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a>ast <span class="op">=</span> plum.get(<span class="st">&#39;AST&#39;</span>)</span>
+<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>shuffled <span class="op">=</span> plum.assign(Won_shuffled<span class="op">=</span>np.random.permutation(won)) <span class="op">\</span></span>
+<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a>               .assign(AST_shuffled<span class="op">=</span>np.random.permutation(ast))</span></code></pre></div>
 <p>Which of the following options <strong>does not</strong> compute a
 valid simulated test statistic for this permutation test?</p>
 <ul class="task-list">
@@ -3855,20 +3904,21 @@ <h3 id="problem-16.1">Problem 16.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading16_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_1" aria-expanded="true" aria-controls="collapse16_1">
+<h2 class="accordion-header" id="heading16_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_2" aria-expanded="true" aria-controls="collapse16_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse16_1" class="accordion-collapse collapse"
-aria-labelledby="heading16_1" data-bs-parent="#accordionExample">
+<div id="collapse16_2" class="accordion-collapse collapse"
+aria-labelledby="heading16_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer:</strong>
 <code>diff_in_group_means(shuffled, 'Won', 'AST')</code></p>
-<p><code>diff_in_group_means(shuffled, 'Won', 'AST')</code> computes the
+<p>As we saw in the previous subpart,
+<code>diff_in_group_means(shuffled, 'Won', 'AST')</code> computes the
 observed test statistic, which is -0.61. There is no randomness involved
 in the observed test statistic; each time we run the line
 <code>diff_in_group_means(shuffled, 'Won', 'AST')</code> we will see the
@@ -3899,9 +3949,9 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-16.2">Problem 16.2</h3>
+<h3 id="problem-16.3">Problem 16.3</h3>
 <p>Suppose we generate 10,000 simulated test statistics, using one of
-the valid options from Question 1.1. The empirical distribution of test
+the valid options from Question 4.2. The empirical distribution of test
 statistics, with a red line at <code>observed_diff</code>, is shown
 below.</p>
 <center><img src='../../assets/images/wi22-final/quarter-hist.png' width=50%></center>
@@ -3925,13 +3975,13 @@ <h3 id="problem-16.2">Problem 16.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading16_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_2" aria-expanded="true" aria-controls="collapse16_2">
+<h2 class="accordion-header" id="heading16_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_3" aria-expanded="true" aria-controls="collapse16_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse16_2" class="accordion-collapse collapse"
-aria-labelledby="heading16_2" data-bs-parent="#accordionExample">
+<div id="collapse16_3" class="accordion-collapse collapse"
+aria-labelledby="heading16_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3984,70 +4034,59 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<hr />
-<h2 id="problem-17">Problem 17</h2>
-<p>Consider the definition of the function
-<code>diff_in_group_means</code>:</p>
-<div class="sourceCode" id="cb31"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> diff_in_group_means(df, group_col, num_col):</span>
-<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>    s <span class="op">=</span> df.groupby(group_col).mean().get(num_col)</span>
-<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> s.loc[<span class="va">False</span>] <span class="op">-</span> s.loc[<span class="va">True</span>]</span></code></pre></div>
-<p><br></p>
-<h3 id="problem-17.1">Problem 17.1</h3>
-<p>It turns out that Kelsey Plum averages 0.61 more assists in games
-that she wins (“winning games”) than in games that she loses (“losing
-games”). Fill in the blanks below so that <code>observed_diff</code>
-evaluates to -0.61.</p>
-<div class="sourceCode" id="cb32"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>observed_diff <span class="op">=</span> diff_in_group_means(plum, __(a)__, __(b)__)</span></code></pre></div>
-<ol type="1">
-<li><p>What goes in blank (a)?</p></li>
-<li><p>What goes in blank (b)?</p></li>
-</ol>
+<h3 id="problem-16.4">Problem 16.4</h3>
+<p><strong>True or False:</strong> The histogram drawn in the previous
+subpart is a density histogram.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading17_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_1" aria-expanded="true" aria-controls="collapse17_1">
+<h2 class="accordion-header" id="heading16_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_4" aria-expanded="true" aria-controls="collapse16_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse17_1" class="accordion-collapse collapse"
-aria-labelledby="heading17_1" data-bs-parent="#accordionExample">
+<div id="collapse16_4" class="accordion-collapse collapse"
+aria-labelledby="heading16_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answers:</strong> <code>'Won'</code>, <code>'AST'</code></p>
-<p>To compute the number of assists Kelsey Plum averages in winning and
-losing games, we need to group by <code>'Won'</code>. Once doing so, and
-using the <code>.mean()</code> aggregation method, we need to access
-elements in the <code>'AST'</code> column.</p>
-<p>The second argument to <code>diff_in_group_means</code>,
-<code>group_col</code>, is the column we’re grouping by, and so blank
-(a) must be filled by <code>'Won'</code>. Then, the second argument,
-<code>num_col</code>, must be <code>'AST'</code>.</p>
-<p>Note that after extracting the Series containing the average number
-of assists in wins and losses, we are returning the value with the index
-<code>False</code> (“loss”) minus the value with the index
-<code>True</code> (“win”). So, throughout this problem, keep in mind
-that we are computing “losses minus wins”. Since our observation was
-that she averaged 0.61 more assists in wins than in losses, it makes
-sense that <code>diff_in_group_means(plum, 'Won', 'AST')</code> is -0.61
-(rather than +0.61).</p>
+<p><strong>Answer:</strong> False</p>
+<p>The area of a density histogram is 1. The area of the histogram drawn
+in the previous subpart is much larger than 1. In fact, the area of this
+histogram is in the hundreds or thousands; you can draw a rectangle
+stretching from -1 to 1 on the <span class="math inline">x</span>-axis
+and 0 to 300 on the <span class="math inline">y</span>-axis that has
+area <span class="math inline">2 \cdot 300 = 600</span>, and this
+rectangle is much smaller than the larger histogram.</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 94%.</p>
+<p>The average score on this problem was 82%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-17.2">Problem 17.2</h3>
-<p>After observing that Kelsey Plum averages more assists in winning
-games than in losing games, we become interested in conducting a
-permutation test for the following hypotheses:</p>
+<hr />
+<h2 id="problem-17">Problem 17</h2>
+<p>Consider the definition of the function
+<code>diff_in_group_means</code>:</p>
+<div class="sourceCode" id="cb32"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> diff_in_group_means(df, group_col, num_col):</span>
+<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a>    s <span class="op">=</span> df.groupby(group_col).mean().get(num_col)</span>
+<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> s.loc[<span class="va">False</span>] <span class="op">-</span> s.loc[<span class="va">True</span>]</span></code></pre></div>
+<p><br></p>
+<h3 id="problem-17.1">Problem 17.1</h3>
+<p>It turns out that Kelsey Plum averages 0.61 more assists in games
+that she wins than in games that she loses. After observing that Kelsey
+Plum averages more assists in winning games than in losing games, we
+become interested in conducting a permutation test for the following
+hypotheses:</p>
 <ul>
 <li><strong>Null Hypothesis:</strong> The number of assists Kelsey Plum
 makes in winning games and in losing games come from the same
@@ -4076,21 +4115,20 @@ <h3 id="problem-17.2">Problem 17.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading17_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_2" aria-expanded="true" aria-controls="collapse17_2">
+<h2 class="accordion-header" id="heading17_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_1" aria-expanded="true" aria-controls="collapse17_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse17_2" class="accordion-collapse collapse"
-aria-labelledby="heading17_2" data-bs-parent="#accordionExample">
+<div id="collapse17_1" class="accordion-collapse collapse"
+aria-labelledby="heading17_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer:</strong>
 <code>diff_in_group_means(shuffled, 'Won', 'AST')</code></p>
-<p>As we saw in the previous subpart,
-<code>diff_in_group_means(shuffled, 'Won', 'AST')</code> computes the
+<p><code>diff_in_group_means(shuffled, 'Won', 'AST')</code> computes the
 observed test statistic, which is -0.61. There is no randomness involved
 in the observed test statistic; each time we run the line
 <code>diff_in_group_means(shuffled, 'Won', 'AST')</code> we will see the
@@ -4121,9 +4159,9 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-17.3">Problem 17.3</h3>
+<h3 id="problem-17.2">Problem 17.2</h3>
 <p>Suppose we generate 10,000 simulated test statistics, using one of
-the valid options from part 1. The empirical distribution of test
+the valid options from Question 1.1. The empirical distribution of test
 statistics, with a red line at <code>observed_diff</code>, is shown
 below.</p>
 <center><img src='../../assets/images/wi22-final/quarter-hist.png' width=50%></center>
@@ -4147,13 +4185,13 @@ <h3 id="problem-17.3">Problem 17.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading17_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_3" aria-expanded="true" aria-controls="collapse17_3">
+<h2 class="accordion-header" id="heading17_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_2" aria-expanded="true" aria-controls="collapse17_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse17_3" class="accordion-collapse collapse"
-aria-labelledby="heading17_3" data-bs-parent="#accordionExample">
+<div id="collapse17_2" class="accordion-collapse collapse"
+aria-labelledby="heading17_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4345,7 +4383,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <h3 id="problem-18.3">Problem 18.3</h3>
 <p>Suppose we generate 10,000 simulated test statistics, using one of
-the valid options from Question 4.2. The empirical distribution of test
+the valid options from part 1. The empirical distribution of test
 statistics, with a red line at <code>observed_diff</code>, is shown
 below.</p>
 <center><img src='../../assets/images/wi22-final/quarter-hist.png' width=50%></center>
@@ -4428,44 +4466,6 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-18.4">Problem 18.4</h3>
-<p><strong>True or False:</strong> The histogram drawn in the previous
-subpart is a density histogram.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading18_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse18_4" aria-expanded="true" aria-controls="collapse18_4">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse18_4" class="accordion-collapse collapse"
-aria-labelledby="heading18_4" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> False</p>
-<p>The area of a density histogram is 1. The area of the histogram drawn
-in the previous subpart is much larger than 1. In fact, the area of this
-histogram is in the hundreds or thousands; you can draw a rectangle
-stretching from -1 to 1 on the <span class="math inline">x</span>-axis
-and 0 to 300 on the <span class="math inline">y</span>-axis that has
-area <span class="math inline">2 \cdot 300 = 600</span>, and this
-rectangle is much smaller than the larger histogram.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 82%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
 <hr />
 <p class="meta"><em>Source:</em> wi23-final — Q4</p>
 <h2 id="problem-19">Problem 19</h2>
diff --git a/docs/lectures/lec23/index.html b/docs/lectures/lec23/index.html
index cd390c6..5ae5f08 100644
--- a/docs/lectures/lec23/index.html
+++ b/docs/lectures/lec23/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/lectures/lec24/index.html b/docs/lectures/lec24/index.html
index a495860..5e75b97 100644
--- a/docs/lectures/lec24/index.html
+++ b/docs/lectures/lec24/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -1761,9 +1761,16 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-9">Problem 9</h2>
-<p><strong>True or False</strong>: The slope of the regression line,
-when both variables are measured in original units, is never more than
-1.</p>
+<p><em>Does an ice cream shop sell more chocolate or vanilla ice cream
+cones?</em></p>
+<p>Choose the best data science tool to help you answer this
+question.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> hypothesis testing</p></li>
+<li><p><input type="radio" disabled="" /> permutation (A/B) testing</p></li>
+<li><p><input type="radio" disabled="" /> Central Limit Theorem</p></li>
+<li><p><input type="radio" disabled="" /> regression</p></li>
+</ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading9">
@@ -1777,28 +1784,48 @@ <h2 class="accordion-header" id="heading9">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> False</p>
-<p>Original units refers to units as they are. Clearly, regression
-slopes can be greater than 1 (for example if for every change in 1 unit
-of x corresponds to a change in 20 units of y the slope will be 20).</p>
+<p><strong>Answer: </strong> hypothesis testing</p>
+<p>The question at hand is dealing with differences between sales of
+different flavors of ice cream, which is the same thing as the total of
+ice cream cones sold. We can use hypothesis testing to test our null
+hypothesis that the count of Vanilla cones sold is higher than
+Chocolate, and our alternative hypothesis that the count of Chocolate
+cones sold is more than Vanilla. A permutation test is not suitable here
+because we are not comparing any numerical quantity associated with each
+group. A permutation test could be used to answer questions like “Are
+chocolate ice cream cones more expensive than vanilla ice cream cones?”
+or “Do chocolate ice cream cones have more calories than vanilla ice
+cream cones?”, or any other question where you are tracking a number
+(cost or calories) along with each ice cream cone. In our case, however,
+we are not tracking a number along with each individual ice cream cone,
+but instead tracking a total of ice cream cones sold.</p>
+<p>An analogy to this hypothesis test can be found in the “fair or
+unfair coin” problem in Lectures 20 and 21, where our null hypothesis is
+that the coin is fair and our alternative hypothesis is that the coin is
+unfair. The “fairness” of the coin is not a numerical quantity that we
+can track with each individual coin flip, just like how the count of ice
+cream cones sold is not a numerical quantity that we can track with each
+individual ice cream cone.</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 96%.</p>
+<p>The average score on this problem was 57%.</p>
 </div>
 </div>
 </div>
 </div>
 <hr />
 <h2 id="problem-10">Problem 10</h2>
-<p>A restaurant keeps track of each table’s number of people (average 3;
-standard deviation 1) and the amount of the bill (average $60, standard
-deviation $12). If the number of people and amount of the bill are
-linearly associated with correlation 0.8, what is the predicted bill for
-a table of 5 people? Input your answer below, <strong>to the nearest
-cent</strong>. Make sure your answer is just a number and does not
-include the $ symbol or any text.</p>
+<p><em>Are nonfiction books longer than fiction books?</em></p>
+<p>Choose the best data science tool to help you answer this
+question.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> hypothesis testing</p></li>
+<li><p><input type="radio" disabled="" /> permutation (A/B) testing</p></li>
+<li><p><input type="radio" disabled="" /> Central Limit Theorem</p></li>
+<li><p><input type="radio" disabled="" /> regression</p></li>
+</ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading10">
@@ -1812,32 +1839,24 @@ <h2 class="accordion-header" id="heading10">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> 79.20</p>
-<p>To answer this question, first find the z score for a table of 5
-people. Z = (5-3)/1 = 2. Now having this Z score, find the price that
-correlated in the bill distribution by finding the value for 2 standard
-deviations larger than the mean while also accounting for the
-correlation between the two variables. This is calculated with mean +
-((Z<em>SD) </em> r) which is 60 + ((12 * 2) * 0.8) = 79.20.</p>
-<p>Alternatively, we could solve for the regression line and plug our
-values in according to the reference sheet:</p>
-<p>m = (0.8) * (12/1) and b = 60 - (48/5) * 3 (where m is the slope and
-b is the y-intercept)</p>
-<p>Thus plugging the appropriate values in our regression line
-yields</p>
-<p>y = (48/5) * 5 + 60 - (48/5)*3 = 79.2</p>
+<p><strong>Answer: </strong> permutation (A/B) testing</p>
+<p>The question <em>Are nonfiction books longer than fiction books?</em>
+is investigating the difference between two underlying populations
+(nonfiction books and fiction books). A permutation test is the best
+data science tool when investigating differences between two underlying
+distributions.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 88%.</p>
+<p>The average score on this problem was 90%.</p>
 </div>
 </div>
 </div>
 </div>
 <hr />
 <h2 id="problem-11">Problem 11</h2>
-<p><em>Are nonfiction books longer than fiction books?</em></p>
+<p><em>Do people have more friends as they get older?</em></p>
 <p>Choose the best data science tool to help you answer this
 question.</p>
 <ul class="task-list">
@@ -1859,12 +1878,11 @@ <h2 class="accordion-header" id="heading11">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> permutation (A/B) testing</p>
-<p>The question <em>Are nonfiction books longer than fiction books?</em>
-is investigating the difference between two underlying populations
-(nonfiction books and fiction books). A permutation test is the best
-data science tool when investigating differences between two underlying
-distributions.</p>
+<p><strong>Answer: </strong> regression</p>
+<p>The question at hand is investigating two continuous variables (time
+and number of friends). Regression is the best data science tool as it
+is dealing with two continuous variables and we can understand
+correlations between time and the number of friends.</p>
 <hr/>
 <h5>Difficulty: ⭐️</h5>
 <p>
@@ -1876,15 +1894,13 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-12">Problem 12</h2>
-<p><em>Do people have more friends as they get older?</em></p>
-<p>Choose the best data science tool to help you answer this
-question.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> hypothesis testing</p></li>
-<li><p><input type="radio" disabled="" /> permutation (A/B) testing</p></li>
-<li><p><input type="radio" disabled="" /> Central Limit Theorem</p></li>
-<li><p><input type="radio" disabled="" /> regression</p></li>
-</ul>
+<p>A restaurant keeps track of each table’s number of people (average 3;
+standard deviation 1) and the amount of the bill (average $60, standard
+deviation $12). If the number of people and amount of the bill are
+linearly associated with correlation 0.8, what is the predicted bill for
+a table of 5 people? Input your answer below, <strong>to the nearest
+cent</strong>. Make sure your answer is just a number and does not
+include the $ symbol or any text.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading12">
@@ -1898,32 +1914,34 @@ <h2 class="accordion-header" id="heading12">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> regression</p>
-<p>The question at hand is investigating two continuous variables (time
-and number of friends). Regression is the best data science tool as it
-is dealing with two continuous variables and we can understand
-correlations between time and the number of friends.</p>
+<p><strong>Answer: </strong> 79.20</p>
+<p>To answer this question, first find the z score for a table of 5
+people. Z = (5-3)/1 = 2. Now having this Z score, find the price that
+correlated in the bill distribution by finding the value for 2 standard
+deviations larger than the mean while also accounting for the
+correlation between the two variables. This is calculated with mean +
+((Z<em>SD) </em> r) which is 60 + ((12 * 2) * 0.8) = 79.20.</p>
+<p>Alternatively, we could solve for the regression line and plug our
+values in according to the reference sheet:</p>
+<p>m = (0.8) * (12/1) and b = 60 - (48/5) * 3 (where m is the slope and
+b is the y-intercept)</p>
+<p>Thus plugging the appropriate values in our regression line
+yields</p>
+<p>y = (48/5) * 5 + 60 - (48/5)*3 = 79.2</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 90%.</p>
+<p>The average score on this problem was 88%.</p>
 </div>
 </div>
 </div>
 </div>
 <hr />
 <h2 id="problem-13">Problem 13</h2>
-<p><em>Does an ice cream shop sell more chocolate or vanilla ice cream
-cones?</em></p>
-<p>Choose the best data science tool to help you answer this
-question.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> hypothesis testing</p></li>
-<li><p><input type="radio" disabled="" /> permutation (A/B) testing</p></li>
-<li><p><input type="radio" disabled="" /> Central Limit Theorem</p></li>
-<li><p><input type="radio" disabled="" /> regression</p></li>
-</ul>
+<p><strong>True or False</strong>: The slope of the regression line,
+when both variables are measured in original units, is never more than
+1.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading13">
@@ -1937,33 +1955,15 @@ <h2 class="accordion-header" id="heading13">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> hypothesis testing</p>
-<p>The question at hand is dealing with differences between sales of
-different flavors of ice cream, which is the same thing as the total of
-ice cream cones sold. We can use hypothesis testing to test our null
-hypothesis that the count of Vanilla cones sold is higher than
-Chocolate, and our alternative hypothesis that the count of Chocolate
-cones sold is more than Vanilla. A permutation test is not suitable here
-because we are not comparing any numerical quantity associated with each
-group. A permutation test could be used to answer questions like “Are
-chocolate ice cream cones more expensive than vanilla ice cream cones?”
-or “Do chocolate ice cream cones have more calories than vanilla ice
-cream cones?”, or any other question where you are tracking a number
-(cost or calories) along with each ice cream cone. In our case, however,
-we are not tracking a number along with each individual ice cream cone,
-but instead tracking a total of ice cream cones sold.</p>
-<p>An analogy to this hypothesis test can be found in the “fair or
-unfair coin” problem in Lectures 20 and 21, where our null hypothesis is
-that the coin is fair and our alternative hypothesis is that the coin is
-unfair. The “fairness” of the coin is not a numerical quantity that we
-can track with each individual coin flip, just like how the count of ice
-cream cones sold is not a numerical quantity that we can track with each
-individual ice cream cone.</p>
+<p><strong>Answer: </strong> False</p>
+<p>Original units refers to units as they are. Clearly, regression
+slopes can be greater than 1 (for example if for every change in 1 unit
+of x corresponds to a change in 20 units of y the slope will be 20).</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 57%.</p>
+<p>The average score on this problem was 96%.</p>
 </div>
 </div>
 </div>
diff --git a/docs/lectures/lec25/index.html b/docs/lectures/lec25/index.html
index 04d70c6..9b4fe82 100644
--- a/docs/lectures/lec25/index.html
+++ b/docs/lectures/lec25/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -337,144 +337,11 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-2">Problem 2</h2>
-<p>Suppose the price of an IKEA product and the cost to have it
-assembled are linearly associated with a correlation of 0.8. Product
-prices have a mean of 140 dollars and a standard deviation of 40
-dollars. Assembly costs have a mean of 80 dollars and a standard
-deviation of 10 dollars. We want to predict the assembly cost of a
-product based on its price using linear regression.</p>
-<p><br></p>
-<h3 id="problem-2.1">Problem 2.1</h3>
-<p>The NORDMELA 4-drawer dresser sells for 200 dollars. How much do we
-predict its assembly cost to be?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading2_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_1" aria-expanded="true" aria-controls="collapse2_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse2_1" class="accordion-collapse collapse"
-aria-labelledby="heading2_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-
-</header>
-<p><strong>Answer: </strong> 92 dollars</p>
-<p>We first use the formulas for the slope, <span class="math inline">m</span>, and intercept, <span class="math inline">b</span>, of the regression line to find the
-equation. For our application, <span class="math inline">x</span> is the
-price and <span class="math inline">y</span> is the assembly cost since
-we want to predict the assembly cost based on price.</p>
-<p><span class="math display">\begin{aligned}
-        m &amp;= r*\frac{\text{SD of }y}{\text{SD of }x} \\
-                     &amp;= 0.8*\frac{10}{40} \\
-                     &amp;= 0.2\\
-        b &amp;= \text{mean of }y - m*\text{mean of }x  \\
-                     &amp;= 80 - 0.2*140 \\
-                     &amp;= 80 - 28 \\
-                     &amp;= 52
-\end{aligned}</span></p>
-<p>Now we know the formula of the regression line and we simply plug in
-<span class="math inline">x=200</span> to find the associated <span class="math inline">y</span> value.</p>
-<p><span class="math display">\begin{aligned}
-        y &amp;= mx+b \\
-        y &amp;= 0.2x+52 \\
-         &amp;= 0.2*200+52 \\
-         &amp;= 92
-\end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 76%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-2.2">Problem 2.2</h3>
-<p>The IDANÄS wardrobe sells for 80 dollars more than the KLIPPAN
-loveseat, so we expect the IDANÄS wardrobe will have a greater assembly
-cost than the KLIPPAN loveseat. How much do we predict the difference in
-assembly costs to be?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading2_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_2" aria-expanded="true" aria-controls="collapse2_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse2_2" class="accordion-collapse collapse"
-aria-labelledby="heading2_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-
-</header>
-<p><strong>Answer: </strong> 16 dollars</p>
-<p>The slope of a line describes the change in <span class="math inline">y</span> for each change of 1 in <span class="math inline">x</span>. The difference in <span class="math inline">x</span> values for these two products is 80, so the
-difference in <span class="math inline">y</span> values is <span class="math inline">m*80 = 0.2*80 = 16</span> dollars.</p>
-<p>An equivalent way to state this is:</p>
-<p><span class="math display">\begin{aligned}
-        m &amp;= \frac{\text{ rise, or change in } y}{\text{ run, or
-change in } x} \\
-        0.2 &amp;= \frac{\text{ rise, or change in } y}{80} \\
-        0.2*80 &amp;= \text{ rise, or change in } y \\
-    16 &amp;= \text{ rise, or change in } y
-\end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 65%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-2.3">Problem 2.3</h3>
-<p>If we create a 95% prediction interval for the assembly cost of a 100
-dollar product and another 95% prediction interval for the assembly cost
-of a 120 dollar product, which prediction interval will be wider?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> The one for the 100 dollar product.</p></li>
-<li><p><input type="radio" disabled="" /> The one for the 120 dollar product.</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading2_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_3" aria-expanded="true" aria-controls="collapse2_3">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse2_3" class="accordion-collapse collapse"
-aria-labelledby="heading2_3" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-
-</header>
-<p><strong>Answer: </strong> The one for the 100 dollar product.</p>
-<p>Prediction intervals get wider the further we get from the point
-<span class="math inline">(\text{mean of } x, \text{mean of } y)</span>
-since all regression lines must go through this point. Since the average
-product price is 140 dollars, the prediction interval will be wider for
-the 100 dollar product, since it’s the further of 100 and 120 from 140.
-</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
-<p>The average score on this problem
-was 45%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
-<h2 id="problem-3">Problem 3</h2>
 <p>For each IKEA desk, we know the cost of producing the desk, in
 dollars, and the current sale price of the desk, in dollars. We want to
 predict sale price based on production cost using linear regression.</p>
 <p><br></p>
-<h3 id="problem-3.1">Problem 3.1</h3>
+<h3 id="problem-2.1">Problem 2.1</h3>
 <p>For this scenario, which of the following most likely describes the
 slope of the regression line when both variables are measured in
 dollars?</p>
@@ -486,13 +353,13 @@ <h3 id="problem-3.1">Problem 3.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading3_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_1" aria-expanded="true" aria-controls="collapse3_1">
+<h2 class="accordion-header" id="heading2_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_1" aria-expanded="true" aria-controls="collapse2_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse3_1" class="accordion-collapse collapse"
-aria-labelledby="heading3_1" data-bs-parent="#accordionExample">
+<div id="collapse2_1" class="accordion-collapse collapse"
+aria-labelledby="heading2_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 
@@ -516,7 +383,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-3.2">Problem 3.2</h3>
+<h3 id="problem-2.2">Problem 2.2</h3>
 <p>For this scenario, which of the following most likely describes the
 slope of the regression line when both variables are measured in
 standard units?</p>
@@ -528,13 +395,13 @@ <h3 id="problem-3.2">Problem 3.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading3_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_2" aria-expanded="true" aria-controls="collapse3_2">
+<h2 class="accordion-header" id="heading2_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_2" aria-expanded="true" aria-controls="collapse2_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse3_2" class="accordion-collapse collapse"
-aria-labelledby="heading3_2" data-bs-parent="#accordionExample">
+<div id="collapse2_2" class="accordion-collapse collapse"
+aria-labelledby="heading2_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 
@@ -560,7 +427,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-3.3">Problem 3.3</h3>
+<h3 id="problem-2.3">Problem 2.3</h3>
 <p>The residual plot for this regression is shown below.</p>
 <center><img src='../../assets/images/sp22-final/resid.png' width=40%></center>
 <p>What is being represented on the horizontal axis of the residual
@@ -573,13 +440,13 @@ <h3 id="problem-3.3">Problem 3.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading3_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_3" aria-expanded="true" aria-controls="collapse3_3">
+<h2 class="accordion-header" id="heading2_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_3" aria-expanded="true" aria-controls="collapse2_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse3_3" class="accordion-collapse collapse"
-aria-labelledby="heading3_3" data-bs-parent="#accordionExample">
+<div id="collapse2_3" class="accordion-collapse collapse"
+aria-labelledby="heading2_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 
@@ -600,7 +467,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-3.4">Problem 3.4</h3>
+<h3 id="problem-2.4">Problem 2.4</h3>
 <p>Which of the following is a correct conclusion based on this residual
 plot? Select all that apply.</p>
 <ul class="task-list">
@@ -615,13 +482,13 @@ <h3 id="problem-3.4">Problem 3.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading3_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_4" aria-expanded="true" aria-controls="collapse3_4">
+<h2 class="accordion-header" id="heading2_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse2_4" aria-expanded="true" aria-controls="collapse2_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse3_4" class="accordion-collapse collapse"
-aria-labelledby="heading3_4" data-bs-parent="#accordionExample">
+<div id="collapse2_4" class="accordion-collapse collapse"
+aria-labelledby="heading2_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 
@@ -665,6 +532,139 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-3">Problem 3</h2>
+<p>Suppose the price of an IKEA product and the cost to have it
+assembled are linearly associated with a correlation of 0.8. Product
+prices have a mean of 140 dollars and a standard deviation of 40
+dollars. Assembly costs have a mean of 80 dollars and a standard
+deviation of 10 dollars. We want to predict the assembly cost of a
+product based on its price using linear regression.</p>
+<p><br></p>
+<h3 id="problem-3.1">Problem 3.1</h3>
+<p>The NORDMELA 4-drawer dresser sells for 200 dollars. How much do we
+predict its assembly cost to be?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading3_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_1" aria-expanded="true" aria-controls="collapse3_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse3_1" class="accordion-collapse collapse"
+aria-labelledby="heading3_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+
+</header>
+<p><strong>Answer: </strong> 92 dollars</p>
+<p>We first use the formulas for the slope, <span class="math inline">m</span>, and intercept, <span class="math inline">b</span>, of the regression line to find the
+equation. For our application, <span class="math inline">x</span> is the
+price and <span class="math inline">y</span> is the assembly cost since
+we want to predict the assembly cost based on price.</p>
+<p><span class="math display">\begin{aligned}
+        m &amp;= r*\frac{\text{SD of }y}{\text{SD of }x} \\
+                     &amp;= 0.8*\frac{10}{40} \\
+                     &amp;= 0.2\\
+        b &amp;= \text{mean of }y - m*\text{mean of }x  \\
+                     &amp;= 80 - 0.2*140 \\
+                     &amp;= 80 - 28 \\
+                     &amp;= 52
+\end{aligned}</span></p>
+<p>Now we know the formula of the regression line and we simply plug in
+<span class="math inline">x=200</span> to find the associated <span class="math inline">y</span> value.</p>
+<p><span class="math display">\begin{aligned}
+        y &amp;= mx+b \\
+        y &amp;= 0.2x+52 \\
+         &amp;= 0.2*200+52 \\
+         &amp;= 92
+\end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 76%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-3.2">Problem 3.2</h3>
+<p>The IDANÄS wardrobe sells for 80 dollars more than the KLIPPAN
+loveseat, so we expect the IDANÄS wardrobe will have a greater assembly
+cost than the KLIPPAN loveseat. How much do we predict the difference in
+assembly costs to be?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading3_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_2" aria-expanded="true" aria-controls="collapse3_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse3_2" class="accordion-collapse collapse"
+aria-labelledby="heading3_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+
+</header>
+<p><strong>Answer: </strong> 16 dollars</p>
+<p>The slope of a line describes the change in <span class="math inline">y</span> for each change of 1 in <span class="math inline">x</span>. The difference in <span class="math inline">x</span> values for these two products is 80, so the
+difference in <span class="math inline">y</span> values is <span class="math inline">m*80 = 0.2*80 = 16</span> dollars.</p>
+<p>An equivalent way to state this is:</p>
+<p><span class="math display">\begin{aligned}
+        m &amp;= \frac{\text{ rise, or change in } y}{\text{ run, or
+change in } x} \\
+        0.2 &amp;= \frac{\text{ rise, or change in } y}{80} \\
+        0.2*80 &amp;= \text{ rise, or change in } y \\
+    16 &amp;= \text{ rise, or change in } y
+\end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 65%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-3.3">Problem 3.3</h3>
+<p>If we create a 95% prediction interval for the assembly cost of a 100
+dollar product and another 95% prediction interval for the assembly cost
+of a 120 dollar product, which prediction interval will be wider?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> The one for the 100 dollar product.</p></li>
+<li><p><input type="radio" disabled="" /> The one for the 120 dollar product.</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading3_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse3_3" aria-expanded="true" aria-controls="collapse3_3">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse3_3" class="accordion-collapse collapse"
+aria-labelledby="heading3_3" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+
+</header>
+<p><strong>Answer: </strong> The one for the 100 dollar product.</p>
+<p>Prediction intervals get wider the further we get from the point
+<span class="math inline">(\text{mean of } x, \text{mean of } y)</span>
+since all regression lines must go through this point. Since the average
+product price is 140 dollars, the prediction interval will be wider for
+the 100 dollar product, since it’s the further of 100 and 120 from 140.
+</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
+<p>The average score on this problem
+was 45%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
 <p class="meta"><em>Source:</em> sp24-final — Q12</p>
 <h2 id="problem-4">Problem 4</h2>
 <p>Suppose you know the following information.</p>
diff --git a/docs/lectures/lec3/index.html b/docs/lectures/lec3/index.html
index 7fa2cbf..9a3b408 100644
--- a/docs/lectures/lec3/index.html
+++ b/docs/lectures/lec3/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
 </head>
 <body>
 <header id="title-block-header">
diff --git a/docs/lectures/lec4/index.html b/docs/lectures/lec4/index.html
index 883c8fb..e29a4b4 100644
--- a/docs/lectures/lec4/index.html
+++ b/docs/lectures/lec4/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -551,14 +551,8 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-6">Problem 6</h2>
-<p>Assume you have a DataFrame named <code>ikea</code> that contains
-information about IKEA products, including columns called
-<code>'product'</code>(<code>str</code>): the name of the product,
-<code>'assembly_cost'</code>(<code>int</code>): the assembly cost of
-each product, and <code>'packages'</code>(<code>int</code>): the number
-of packages each product comes in. Complete the expression below so that
-it evaluates to the name of the product for which the average assembly
-cost per package is lowest.</p>
+<p>Complete the expression below so that it evaluates to the name of the
+product for which the average assembly cost per package is lowest.</p>
 <div class="sourceCode" id="cb2"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>(ikea.assign(assembly_per_package <span class="op">=</span> ___(a)___)</span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>     .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_per_package&#39;</span>).___(b)___)</span></code></pre></div>
 <p><br></p>
@@ -627,8 +621,14 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-7">Problem 7</h2>
-<p>Complete the expression below so that it evaluates to the name of the
-product for which the average assembly cost per package is lowest.</p>
+<p>Assume you have a DataFrame named <code>ikea</code> that contains
+information about IKEA products, including columns called
+<code>'product'</code>(<code>str</code>): the name of the product,
+<code>'assembly_cost'</code>(<code>int</code>): the assembly cost of
+each product, and <code>'packages'</code>(<code>int</code>): the number
+of packages each product comes in. Complete the expression below so that
+it evaluates to the name of the product for which the average assembly
+cost per package is lowest.</p>
 <div class="sourceCode" id="cb3"><pre class="sourceCode py"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>(ikea.assign(assembly_per_package <span class="op">=</span> ___(a)___)</span>
 <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>     .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_per_package&#39;</span>).___(b)___)</span></code></pre></div>
 <p><br></p>
@@ -1203,7 +1203,7 @@ <h1 class="title"> </h1>
 first enter. Next, we want the list to go up to the kid’s current age.
 This means we can stop at <code>(age - 10) * (k + 1)</code> to cover all
 of the years beginning from age 12 all the way till their current age.
-Finally, each year the ki adds the same number of tickets one for their
+Finally, each year the kid adds the same number of tickets one for their
 increase in age and another <code>k</code> for food. Thus, the step is
 <code>k + 1</code>.</p>
 <hr/>
@@ -1227,7 +1227,9 @@ <h3 id="problem-12.2">Problem 12.2</h3>
 <code>False</code> means the child never buys food for anyone. The first
 few rows of <code>reaping</code> are shown below, but there are many
 more rows than pictured.</p>
-<center><img src="../../assets/images/sp25-final/reaping_df.jpg" width=300></center>
+<center><img src="https://raw.githubusercontent.com/dsc-courses/practice.dsc10.com/refs/heads/master/assets/images/sp25-final/reaping_df.png" width=300></center>
+<p><br />
+</p>
 <p>Fill in the blanks in the code below to add a new column,
 <code>"tickets"</code>, to <code>reaping</code> that contains the number
 of tickets that the child will have entered into the drawing in the
@@ -1624,90 +1626,13 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-16">Problem 16</h2>
-<p>You are given a DataFrame called <code>sports</code>, indexed by
-<code>'Sport'</code> containing one column,
-<code>'PlayersPerTeam'</code>. The first few rows of the DataFrame are
-shown below:</p>
-<table>
-<thead>
-<tr>
-<th>Sport</th>
-<th>PlayersPerTeam</th>
-</tr>
-</thead>
-<tbody>
-<tr>
-<td>baseball</td>
-<td>9</td>
-</tr>
-<tr>
-<td>basketball</td>
-<td>5</td>
-</tr>
-<tr>
-<td>field hockey</td>
-<td>11</td>
-</tr>
-</tbody>
-</table>
-<p><br /> Which of the following evaluates to
-<code>'basketball'</code>?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> <code>sports.loc[1]</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>sports.iloc[1]</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>sports.index[1]</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>sports.get('Sport').iloc[1]</code></p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading16">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16" aria-expanded="true" aria-controls="collapse16">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse16" class="accordion-collapse collapse"
-aria-labelledby="heading16" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> <code>sports.index[1]</code></p>
-<p>We are told that the DataFrame is indexed by <code>'Sport'</code> and
-<code>'basketball'</code> is one of the elements of the index. To access
-an element of the index, we use <code>.index</code> to extract the index
-and square brackets to extract an element at a certain position.
-Therefore, <code>sports.index[1]</code> will evaluate to
-<code>'basketball'</code>.</p>
-<p>The first two answer choices attempt to use <code>.loc</code> or
-<code>.iloc</code> directly on a DataFrame. We typically use
-<code>.loc</code> or <code>.iloc</code> on a Series that results from
-using <code>.get</code> on some column. Although we don’t typically do
-it this way, it is possible to use <code>.loc</code> or
-<code>.iloc</code> directly on a DataFrame, but doing so would produce
-an entire row of the DataFrame. Since we want just one word,
-<code>'basketball'</code>, the first two answer choices must be
-incorrect.</p>
-<p>The last answer choice is incorrect because we can’t use
-<code>.get</code> with the index, only with a column. The index is never
-considered a column.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 88%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-17">Problem 17</h2>
 <p>Suppose you are given a DataFrame of employees for a given company.
 The DataFrame, called <code>employees</code>, is indexed by
 <code>'employee_id'</code> (string) with a column called
 <code>'years'</code> (int) that contains the number of years each
 employee has worked for the company.</p>
 <p><br></p>
-<h3 id="problem-17.1">Problem 17.1</h3>
+<h3 id="problem-16.1">Problem 16.1</h3>
 <p>Suppose that the code</p>
 <div class="sourceCode" id="cb15"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>employees.sort_values(by<span class="op">=</span><span class="st">&#39;years&#39;</span>, ascending<span class="op">=</span><span class="va">False</span>).index[<span class="dv">0</span>]</span></code></pre></div>
@@ -1721,13 +1646,13 @@ <h3 id="problem-17.1">Problem 17.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading17_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_1" aria-expanded="true" aria-controls="collapse17_1">
+<h2 class="accordion-header" id="heading16_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_1" aria-expanded="true" aria-controls="collapse16_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse17_1" class="accordion-collapse collapse"
-aria-labelledby="heading17_1" data-bs-parent="#accordionExample">
+<div id="collapse16_1" class="accordion-collapse collapse"
+aria-labelledby="heading16_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1755,7 +1680,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-17.2">Problem 17.2</h3>
+<h3 id="problem-16.2">Problem 16.2</h3>
 <p>What will be the output of the following code?</p>
 <div class="sourceCode" id="cb16"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>employees.assign(start<span class="op">=</span><span class="dv">2021</span><span class="op">-</span>employees.get(<span class="st">&#39;years&#39;</span>))</span>
@@ -1770,13 +1695,13 @@ <h3 id="problem-17.2">Problem 17.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading17_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17_2" aria-expanded="true" aria-controls="collapse17_2">
+<h2 class="accordion-header" id="heading16_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse16_2" aria-expanded="true" aria-controls="collapse16_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse17_2" class="accordion-collapse collapse"
-aria-labelledby="heading17_2" data-bs-parent="#accordionExample">
+<div id="collapse16_2" class="accordion-collapse collapse"
+aria-labelledby="heading16_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1804,6 +1729,83 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-17">Problem 17</h2>
+<p>You are given a DataFrame called <code>sports</code>, indexed by
+<code>'Sport'</code> containing one column,
+<code>'PlayersPerTeam'</code>. The first few rows of the DataFrame are
+shown below:</p>
+<table>
+<thead>
+<tr>
+<th>Sport</th>
+<th>PlayersPerTeam</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>baseball</td>
+<td>9</td>
+</tr>
+<tr>
+<td>basketball</td>
+<td>5</td>
+</tr>
+<tr>
+<td>field hockey</td>
+<td>11</td>
+</tr>
+</tbody>
+</table>
+<p><br /> Which of the following evaluates to
+<code>'basketball'</code>?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> <code>sports.loc[1]</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>sports.iloc[1]</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>sports.index[1]</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>sports.get('Sport').iloc[1]</code></p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading17">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse17" aria-expanded="true" aria-controls="collapse17">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse17" class="accordion-collapse collapse"
+aria-labelledby="heading17" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> <code>sports.index[1]</code></p>
+<p>We are told that the DataFrame is indexed by <code>'Sport'</code> and
+<code>'basketball'</code> is one of the elements of the index. To access
+an element of the index, we use <code>.index</code> to extract the index
+and square brackets to extract an element at a certain position.
+Therefore, <code>sports.index[1]</code> will evaluate to
+<code>'basketball'</code>.</p>
+<p>The first two answer choices attempt to use <code>.loc</code> or
+<code>.iloc</code> directly on a DataFrame. We typically use
+<code>.loc</code> or <code>.iloc</code> on a Series that results from
+using <code>.get</code> on some column. Although we don’t typically do
+it this way, it is possible to use <code>.loc</code> or
+<code>.iloc</code> directly on a DataFrame, but doing so would produce
+an entire row of the DataFrame. Since we want just one word,
+<code>'basketball'</code>, the first two answer choices must be
+incorrect.</p>
+<p>The last answer choice is incorrect because we can’t use
+<code>.get</code> with the index, only with a column. The index is never
+considered a column.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 88%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <p class="meta"><em>Source:</em> wi23-midterm — Q1</p>
 <h2 id="problem-18">Problem 18</h2>
 <p><br></p>
diff --git a/docs/lectures/lec5/index.html b/docs/lectures/lec5/index.html
index d46a664..b379c39 100644
--- a/docs/lectures/lec5/index.html
+++ b/docs/lectures/lec5/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -2292,12 +2292,15 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-19">Problem 19</h2>
-<p>The following code computes the breed of the cheapest toy dog.</p>
+<p>The following code computes an array containing the unique kinds of
+dogs that are heavier than 20 kg <strong>or</strong> taller than 40 cm
+on average.</p>
 <div class="sourceCode" id="cb30"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>df[__(a)__].__(b)__.__(c)__</span></code></pre></div>
+class="sourceCode py"><code class="sourceCode python"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>foo <span class="op">=</span> df.__(a)__.__(b)__</span>
+<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>np.array(foo[__(c)__].__d__)</span></code></pre></div>
 <p><br></p>
 <h3 id="problem-19.1">Problem 19.1</h3>
-<p>Fill in part (a).</p>
+<p>Fill in blank (a).</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading19_1">
@@ -2311,27 +2314,26 @@ <h2 class="accordion-header" id="heading19_1">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> <code>df.get('kind') == 'toy'</code></p>
-<p>To find the cheapest toy dog, we can start by narrowing down our
-dataframe to only include dogs that are of kind toy. We do this by
-constructing the following boolean condition:
-<code>df.get('kind') == 'toy'</code>, which will check whether a dog is
-of kind toy (i.e. whether or not a given row’s <code>'kind'</code> value
-is equal to <code>'toy'</code>). As a result,
-<code>df[df.get('kind') == 'toy']</code> will retrieve all rows for
-which the <code>'kind'</code> column is equal to <code>'toy'</code>.</p>
+<p><strong>Answer: </strong> <code>groupby('kind')</code></p>
+<p>We start this problem by grouping the dataframe by
+<code>'kind'</code> since we’re only interested in whether each unique
+<code>'kind'</code> of dog fits some sort of constraint. We don’t quite
+perform querying yet since we need to group the DataFrame first. In
+other words, we first need to group the DataFrame into each
+<code>'kind'</code> before we could apply any sort of boolean
+conditionals.</p>
 <hr/>
 <h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 97%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-19.2">Problem 19.2</h3>
-<p>Fill in part (b).</p>
+<p>Fill in blank (b).</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading19_2">
@@ -2345,31 +2347,24 @@ <h2 class="accordion-header" id="heading19_2">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> <code>.sort_values('price')</code></p>
-<p>Next, we can sort the resulting dataframe by price, which will make
-the minimum price (i.e. the cheapest toy dog) easily accessible to us
-later on. To sort the dataframe, simply use <code>.sort_values()</code>,
-with parameter <code>'price'</code> as follows:
-<code>.sort_values('price')</code></p>
+<p><strong>Answer: </strong> <code>.mean()</code></p>
+<p>After we do <code>.groupby('kind')</code>, we need to apply
+<code>.mean()</code> since the problem asks if each unique
+<code>'kind'</code> of dog satisfies certain constraints <strong>on
+average</strong>. <code>.mean()</code> calculates the average of each
+column of each group which is what we want.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 86%.</p>
+<p>The average score on this problem was 94%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-19.3">Problem 19.3</h3>
-<p>Which of the following can fill in blank (c)? <strong>Select all that
-apply.</strong></p>
-<ul class="task-list">
-<li><p><input type="checkbox" disabled="" /> <code>loc[0]</code></p></li>
-<li><p><input type="checkbox" disabled="" /> <code>iloc[0]</code></p></li>
-<li><p><input type="checkbox" disabled="" /> <code>index[0]</code></p></li>
-<li><p><input type="checkbox" disabled="" /> <code>min()</code></p></li>
-</ul>
+<p>Fill in blank (c).</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading19_3">
@@ -2383,30 +2378,94 @@ <h2 class="accordion-header" id="heading19_3">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> <code>index[0]</code></p>
-<ul>
-<li><code>loc[0]</code>: <code>loc</code> retrieves an element by the
-row label, which in this case is by <code>'breed'</code>, not by index
-value. Furthermore, <code>loc</code> actually returns the entire row,
-which is not what we are looking for. (Note that we are trying to find
-the singular <code>'breed'</code> of the cheapest toy dog.)<br/>
-</li>
-<li><code>iloc[0]</code>: While <code>iloc</code> does retrieve elements
-by index position, <code>iloc</code> actually returns the entire row,
-which is not what we are looking for.</li>
-<li><code>index[0]</code>: Note that since <code>'breed'</code> is the
-index column of our dataframe, and since we have already filtered and
-sorted the dataframe, simply taking the <code>'breed'</code> at index 0,
-or <code>index[0]</code> will return the <code>'breed'</code> of the
-cheapest toy dog.</li>
-<li><code>min()</code>: <code>min()</code> is a method used to find the
-smallest value on a series not a dataframe.</li>
+<p><strong>Answer: </strong>
+<code>(foo.get('weight') &gt; 20 | foo.get('height') &gt; 40)</code></p>
+<p>Once we have grouped the dogs by <code>'kind'</code> and have
+calculated the average stats of each kind of dog, we can do some
+querying with two conditionals: <code>foo.get('weight') &gt; 20</code>
+gets the kinds of dogs that are heavier than 20 kg on average and
+<code>foo.get('height') &gt; 40)</code> gets the kinds of dogs that are
+taller than 40 cm on average. We combine these two conditions with the
+<code>|</code> operator since we want the kind of dogs that satisfy
+either condition.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 93%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-19.4">Problem 19.4</h3>
+<p>Which of the following should fill in blank (d)?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> <code>.index</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.unique()</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.get('kind')</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.get(['kind'])</code></p></li>
 </ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading19_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_4" aria-expanded="true" aria-controls="collapse19_4">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse19_4" class="accordion-collapse collapse"
+aria-labelledby="heading19_4" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> <code>.index</code></p>
+<p>Note that earlier, we did <code>groupby('kind')</code>, which
+automatically sets each unique <code>'kind'</code> as the index. Since
+this is what we want anyways, simply doing <code>.index</code> will give
+us all the kinds of dogs that satisfy the given conditions.</p>
+<p></p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
+<p>The average score on this problem was
+94%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-19.5">Problem 19.5</h3>
+<p>Let’s say that right after blank (b), we added
+<code>reset_index()</code>. Now, which of the following should fill in
+blank (d)?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> <code>.index</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.unique()</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.get('kind')</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>.get(['kind'])</code></p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading19_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_5" aria-expanded="true" aria-controls="collapse19_5">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse19_5" class="accordion-collapse collapse"
+aria-labelledby="heading19_5" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> <code>.get('kind')</code></p>
+<p>Now that we have reset the index of the dataframe,
+<code>'kind'</code> is once again its own column so we could simply do
+<code>.get('kind')</code>.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 81%.</p>
+<p>The average score on this problem was 100%.</p>
 </div>
 </div>
 </div>
@@ -2558,15 +2617,12 @@ <h5>Difficulty: ⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-21">Problem 21</h2>
-<p>The following code computes an array containing the unique kinds of
-dogs that are heavier than 20 kg <strong>or</strong> taller than 40 cm
-on average.</p>
+<p>The following code computes the breed of the cheapest toy dog.</p>
 <div class="sourceCode" id="cb32"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>foo <span class="op">=</span> df.__(a)__.__(b)__</span>
-<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a>np.array(foo[__(c)__].__d__)</span></code></pre></div>
+class="sourceCode py"><code class="sourceCode python"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>df[__(a)__].__(b)__.__(c)__</span></code></pre></div>
 <p><br></p>
 <h3 id="problem-21.1">Problem 21.1</h3>
-<p>Fill in blank (a).</p>
+<p>Fill in part (a).</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading21_1">
@@ -2580,26 +2636,27 @@ <h2 class="accordion-header" id="heading21_1">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> <code>groupby('kind')</code></p>
-<p>We start this problem by grouping the dataframe by
-<code>'kind'</code> since we’re only interested in whether each unique
-<code>'kind'</code> of dog fits some sort of constraint. We don’t quite
-perform querying yet since we need to group the DataFrame first. In
-other words, we first need to group the DataFrame into each
-<code>'kind'</code> before we could apply any sort of boolean
-conditionals.</p>
+<p><strong>Answer: </strong> <code>df.get('kind') == 'toy'</code></p>
+<p>To find the cheapest toy dog, we can start by narrowing down our
+dataframe to only include dogs that are of kind toy. We do this by
+constructing the following boolean condition:
+<code>df.get('kind') == 'toy'</code>, which will check whether a dog is
+of kind toy (i.e. whether or not a given row’s <code>'kind'</code> value
+is equal to <code>'toy'</code>). As a result,
+<code>df[df.get('kind') == 'toy']</code> will retrieve all rows for
+which the <code>'kind'</code> column is equal to <code>'toy'</code>.</p>
 <hr/>
 <h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 97%.</p>
+<p>The average score on this problem was 91%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-21.2">Problem 21.2</h3>
-<p>Fill in blank (b).</p>
+<p>Fill in part (b).</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading21_2">
@@ -2613,24 +2670,31 @@ <h2 class="accordion-header" id="heading21_2">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> <code>.mean()</code></p>
-<p>After we do <code>.groupby('kind')</code>, we need to apply
-<code>.mean()</code> since the problem asks if each unique
-<code>'kind'</code> of dog satisfies certain constraints <strong>on
-average</strong>. <code>.mean()</code> calculates the average of each
-column of each group which is what we want.</p>
+<p><strong>Answer: </strong> <code>.sort_values('price')</code></p>
+<p>Next, we can sort the resulting dataframe by price, which will make
+the minimum price (i.e. the cheapest toy dog) easily accessible to us
+later on. To sort the dataframe, simply use <code>.sort_values()</code>,
+with parameter <code>'price'</code> as follows:
+<code>.sort_values('price')</code></p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 94%.</p>
+<p>The average score on this problem was 86%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-21.3">Problem 21.3</h3>
-<p>Fill in blank (c).</p>
+<p>Which of the following can fill in blank (c)? <strong>Select all that
+apply.</strong></p>
+<ul class="task-list">
+<li><p><input type="checkbox" disabled="" /> <code>loc[0]</code></p></li>
+<li><p><input type="checkbox" disabled="" /> <code>iloc[0]</code></p></li>
+<li><p><input type="checkbox" disabled="" /> <code>index[0]</code></p></li>
+<li><p><input type="checkbox" disabled="" /> <code>min()</code></p></li>
+</ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading21_3">
@@ -2644,118 +2708,54 @@ <h2 class="accordion-header" id="heading21_3">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong>
-<code>(foo.get('weight') &gt; 20 | foo.get('height') &gt; 40)</code></p>
-<p>Once we have grouped the dogs by <code>'kind'</code> and have
-calculated the average stats of each kind of dog, we can do some
-querying with two conditionals: <code>foo.get('weight') &gt; 20</code>
-gets the kinds of dogs that are heavier than 20 kg on average and
-<code>foo.get('height') &gt; 40)</code> gets the kinds of dogs that are
-taller than 40 cm on average. We combine these two conditions with the
-<code>|</code> operator since we want the kind of dogs that satisfy
-either condition.</p>
+<p><strong>Answer: </strong> <code>index[0]</code></p>
+<ul>
+<li><code>loc[0]</code>: <code>loc</code> retrieves an element by the
+row label, which in this case is by <code>'breed'</code>, not by index
+value. Furthermore, <code>loc</code> actually returns the entire row,
+which is not what we are looking for. (Note that we are trying to find
+the singular <code>'breed'</code> of the cheapest toy dog.)<br/>
+</li>
+<li><code>iloc[0]</code>: While <code>iloc</code> does retrieve elements
+by index position, <code>iloc</code> actually returns the entire row,
+which is not what we are looking for.</li>
+<li><code>index[0]</code>: Note that since <code>'breed'</code> is the
+index column of our dataframe, and since we have already filtered and
+sorted the dataframe, simply taking the <code>'breed'</code> at index 0,
+or <code>index[0]</code> will return the <code>'breed'</code> of the
+cheapest toy dog.</li>
+<li><code>min()</code>: <code>min()</code> is a method used to find the
+smallest value on a series not a dataframe.</li>
+</ul>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 93%.</p>
+<p>The average score on this problem was 81%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-21.4">Problem 21.4</h3>
-<p>Which of the following should fill in blank (d)?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> <code>.index</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.unique()</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.get('kind')</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.get(['kind'])</code></p></li>
-</ul>
+<hr />
+<p class="meta"><em>Source:</em> su24-final — Q1</p>
+<h2 id="problem-22">Problem 22</h2>
+<p><br></p>
+<h3 id="problem-22.1">Problem 22.1</h3>
+<p>Fill in the blanks so that the expression below evaluates to the
+<em>proportion</em> of stages won by the country with the most stage
+wins.</p>
+<div class="sourceCode" id="cb33"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a>    stages.groupby(__(i)__).__(ii)__.get(<span class="st">&quot;Type&quot;</span>).__(iii)__ <span class="op">/</span> stages.shape[<span class="dv">0</span>]</span></code></pre></div>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_4" aria-expanded="true" aria-controls="collapse21_4">
+<h2 class="accordion-header" id="heading22_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse22_1" aria-expanded="true" aria-controls="collapse22_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_4" class="accordion-collapse collapse"
-aria-labelledby="heading21_4" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> <code>.index</code></p>
-<p>Note that earlier, we did <code>groupby('kind')</code>, which
-automatically sets each unique <code>'kind'</code> as the index. Since
-this is what we want anyways, simply doing <code>.index</code> will give
-us all the kinds of dogs that satisfy the given conditions.</p>
-<p></p>
-<hr/>
-<h5>Difficulty: ⭐️</h5>
-<p>The average score on this problem was
-94%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-21.5">Problem 21.5</h3>
-<p>Let’s say that right after blank (b), we added
-<code>reset_index()</code>. Now, which of the following should fill in
-blank (d)?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> <code>.index</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.unique()</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.get('kind')</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>.get(['kind'])</code></p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading21_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_5" aria-expanded="true" aria-controls="collapse21_5">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse21_5" class="accordion-collapse collapse"
-aria-labelledby="heading21_5" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> <code>.get('kind')</code></p>
-<p>Now that we have reset the index of the dataframe,
-<code>'kind'</code> is once again its own column so we could simply do
-<code>.get('kind')</code>.</p>
-<hr/>
-<h5>Difficulty: ⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 100%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
-<p class="meta"><em>Source:</em> su24-final — Q1</p>
-<h2 id="problem-22">Problem 22</h2>
-<p><br></p>
-<h3 id="problem-22.1">Problem 22.1</h3>
-<p>Fill in the blanks so that the expression below evaluates to the
-<em>proportion</em> of stages won by the country with the most stage
-wins.</p>
-<div class="sourceCode" id="cb33"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a>    stages.groupby(__(i)__).__(ii)__.get(<span class="st">&quot;Type&quot;</span>).__(iii)__ <span class="op">/</span> stages.shape[<span class="dv">0</span>]</span></code></pre></div>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading22_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse22_1" aria-expanded="true" aria-controls="collapse22_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse22_1" class="accordion-collapse collapse"
-aria-labelledby="heading22_1" data-bs-parent="#accordionExample">
+<div id="collapse22_1" class="accordion-collapse collapse"
+aria-labelledby="heading22_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3575,22 +3575,19 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-29">Problem 29</h2>
-<p>Below, identify the data type of the result of each of the following
-expressions, or select “error” if you believe the expression results in
-an error.</p>
+<p>In this question, we’ll write code to learn more about the
+skyscrapers in the beautiful city of San Diego. (Unrelated fun fact –
+since the San Diego Airport is so close to downtown, buildings in
+downtown San Diego legally cannot be taller than 152 meters.)</p>
 <p><br></p>
 <h3 id="problem-29.1">Problem 29.1</h3>
+<p>Below, fill in the blank to create a DataFrame, named
+<code>san_tall</code>, consisting of just the skyscrapers in San Diego
+that are over 100 meters tall.</p>
 <div class="sourceCode" id="cb45"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>)</span></code></pre></div>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> int or float</p></li>
-<li><p><input type="radio" disabled="" /> Boolean</p></li>
-<li><p><input type="radio" disabled="" /> string</p></li>
-<li><p><input type="radio" disabled="" /> array</p></li>
-<li><p><input type="radio" disabled="" /> Series</p></li>
-<li><p><input type="radio" disabled="" /> DataFrame</p></li>
-<li><p><input type="radio" disabled="" /> error</p></li>
-</ul>
+class="sourceCode py"><code class="sourceCode python"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a>condition <span class="op">=</span> ______</span>
+<span id="cb45-2"><a href="#cb45-2" aria-hidden="true" tabindex="-1"></a>san_tall <span class="op">=</span> sky[(sky.get(<span class="st">&#39;city&#39;</span>) <span class="op">==</span> <span class="st">&#39;San Diego&#39;</span>) <span class="op">&amp;</span> condition]</span></code></pre></div>
+<p>What goes in the blank?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
 <h2 class="accordion-header" id="heading29_1">
@@ -3604,24 +3601,130 @@ <h2 class="accordion-header" id="heading29_1">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> DataFrame</p>
-<p><code>sky</code> is a DataFrame. All the <code>sort_values</code>
-method does is change the order of the rows in the Series/DataFrame it
-is called on, it does not change the data structure. As such,
-<code>sky.sort_values('height')</code> is also a DataFrame.</p>
+<p><strong>Answer:</strong> <code>sky.get('height') &gt; 100</code></p>
+<p>We need to query for all of the skyscrapers that satisfy two
+conditions – the <code>'city'</code> must be <code>'San Diego'</code>
+and the <code>'height'</code> must be above 100. The first condition was
+already implemented for us, so we just need to construct a Boolean
+Series that implements the second condition.</p>
+<p>Here, we want all of the rows where <code>'height'</code> is above
+100, so we <code>get</code> the <code>'height'</code> column and compare
+it to 100 like so: <code>sky.get('height') &gt; 100</code>.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 87%.</p>
+<p>The average score on this problem was 95%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <h3 id="problem-29.2">Problem 29.2</h3>
+<p>Suppose <code>san_tall</code> from the previous part was created
+correctly. Fill in the blanks so that <code>height_many_floors</code>
+evaluates to the <strong>height (in meters)</strong> of the skyscraper
+with the <strong>most floors</strong>, amongst all skyscrapers in San
+Diego that are over 100 meters tall.</p>
 <div class="sourceCode" id="cb46"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).loc[<span class="dv">0</span>]</span></code></pre></div>
+class="sourceCode py"><code class="sourceCode python"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a>height_many_floors <span class="op">=</span> san_tall.______.iloc[<span class="dv">0</span>]</span></code></pre></div>
+<p>What goes in the blank?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading29_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_2" aria-expanded="true" aria-controls="collapse29_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse29_2" class="accordion-collapse collapse"
+aria-labelledby="heading29_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong>
+<code>sort_values('floors', ascending=False).get('height')</code></p>
+<p>The end of the line given to us is <code>.iloc[0]</code>. We know
+that <code>.iloc[0]</code> extracts the first element in whatever Series
+it is called on, so what comes before <code>.iloc[0]</code> must be a
+Series where the first element is the <code>'height'</code> of the
+skyscraper with the most floors, among all skyscrapers in San Diego that
+are over 100 meters tall. The DataFrame we are working with,
+<code>san_tall</code>, already only has skyscrapers in San Diego that
+are over 100 meters tall.</p>
+<p>This means that in the blank, all we need to do is:</p>
+<ol type="1">
+<li>Sort skyscrapers by <code>'floors'</code> in decreasing order (so
+that the first row is the skyscraper with the most
+<code>'floors'</code>).</li>
+<li>Extract the <code>'height'</code> column.</li>
+</ol>
+<p>As such, a complete answer is
+<code>height_many_floors = san_tall.sort_values('floors', ascending=False).get('height').iloc[0]</code>.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 74%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-29.3">Problem 29.3</h3>
+<p><code>height_many_floors</code>, the value you computed in the
+previous part (2.2) was a number.</p>
+<p><strong>True or False:</strong> Assuming that the DataFrame
+<code>san_tall</code> contains all skyscrapers in San Diego,
+<code>height_many_floors</code> is the height (in meters) of the
+<strong>tallest</strong> skyscraper in San Diego.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading29_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_3" aria-expanded="true" aria-controls="collapse29_3">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse29_3" class="accordion-collapse collapse"
+aria-labelledby="heading29_3" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> False</p>
+<p><code>height_many_floors</code> is the height of the skyscraper with
+the most <code>'floors'</code>. However, this is not necessarily the
+tallest skyscraper (i.e. the skyscraper with the largest
+<code>'height'</code>)! Consider the following scenario:</p>
+<ul>
+<li>Building A: 15 floors, height of 150 feet</li>
+<li>Building B: 20 floors, height of 100 feet</li>
+</ul>
+<p><code>height_many_floors</code> would be 100, but it is not the
+<code>'height'</code> of the taller building.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 84%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-30">Problem 30</h2>
+<p>Below, identify the data type of the result of each of the following
+expressions, or select “error” if you believe the expression results in
+an error.</p>
+<p><br></p>
+<h3 id="problem-30.1">Problem 30.1</h3>
+<div class="sourceCode" id="cb47"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">len</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3633,31 +3736,24 @@ <h3 id="problem-29.2">Problem 29.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading29_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_2" aria-expanded="true" aria-controls="collapse29_2">
+<h2 class="accordion-header" id="heading30_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_1" aria-expanded="true" aria-controls="collapse30_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse29_2" class="accordion-collapse collapse"
-aria-labelledby="heading29_2" data-bs-parent="#accordionExample">
+<div id="collapse30_1" class="accordion-collapse collapse"
+aria-labelledby="heading30_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> error</p>
-<p><code>sky.sort_values('height')</code> is a DataFrame, and
-<code>sky.sort_values('height').get('material')</code> is a Series
-corresponding to the <code>'material'</code> column, sorted by
-<code>'height'</code> in increasing order. So far, there are no
-errors.</p>
-<p>Remember, the <code>.loc</code> <em>accessor</em> is used to access
-elements in a Series based on their index.
-<code>sky.sort_values('height').get('material').loc[0]</code> is asking
-for the element in the
-<code>sky.sort_values('height').get('material')</code> Series with index
-0. However, the index of <code>sky</code> is made up of building names.
-Since there is no building named <code>0</code>, <code>.loc[0]</code>
-causes an error.</p>
+<p><strong>Answer:</strong> Series</p>
+<p>The <code>.apply</code> method takes in a function and evaluates that
+function on every element in a Series. Here,
+<code>sky.get('city').apply(len)</code> is using the function
+<code>len</code> on every element in the Series
+<code>sky.get('city')</code>. The result is also a Series, containing
+the lengths of the names of each <code>'city'</code>.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
@@ -3668,9 +3764,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-29.3">Problem 29.3</h3>
-<div class="sourceCode" id="cb47"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).iloc[<span class="dv">0</span>]</span></code></pre></div>
+<h3 id="problem-30.2">Problem 30.2</h3>
+<div class="sourceCode" id="cb48"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">max</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3682,31 +3778,42 @@ <h3 id="problem-29.3">Problem 29.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading29_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_3" aria-expanded="true" aria-controls="collapse29_3">
+<h2 class="accordion-header" id="heading30_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_2" aria-expanded="true" aria-controls="collapse30_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse29_3" class="accordion-collapse collapse"
-aria-labelledby="heading29_3" data-bs-parent="#accordionExample">
+<div id="collapse30_2" class="accordion-collapse collapse"
+aria-labelledby="heading30_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> string</p>
-<p>As we mentioned above,
-<code>sky.sort_values('height').get('material')</code> is a Series
-containing values from the <code>'material'</code> column (but sorted).
-Remember, there is no element in this Series with an index of 0, so
-<code>sky.sort_values('height').get('material').loc[0]</code> errors.
-However, <code>.iloc[0]</code> works differently than
-<code>.loc[0]</code>; <code>.iloc[0]</code> will give us the first
-element in a Series (independent of what’s in the index). So,
-<code>sky.sort_values('height').get('material').iloc[0]</code> gives us
-back a value from the <code>'material'</code> column, which is made up
-of strings, so it gives us a string. (Specifically, it gives us the
-<code>'material'</code> type of the skyscraper with the smallest
-<code>'height'</code>.)</p>
+<p><strong>Answer:</strong> Series</p>
+<p>This is a tricky problem!</p>
+<p>The function that <code>apply</code> takes in must work on individual
+elements in a Series, i.e. it must work with just a single argument. We
+saw this in the above subpart, where
+<code>sky.get('city').apply(len)</code> applied <code>len</code> on each
+<code>'city'</code> name.</p>
+<p>Here, we are trying to apply the <code>max</code> function on each
+<code>'city'</code> name. The <code>max</code> of a single item does not
+work in Python, because taking the <code>max</code> requires comparing
+two or more elements. Try it out - in a notebook, run the expression
+<code>max(5)</code>, and you’ll see an error. So, if we tried to use
+<code>.apply(max)</code> on a Series of numbers, we’d run into an
+error.</p>
+<p><strong>However</strong>, we are using <code>.apply(max)</code> on a
+Series of strings, and it turns out that Python <strong>does</strong>
+allow us to take the <code>max</code> of a string! The <code>max</code>
+of a string in Python is defined as the last character in the string
+alphabetically, so <code>max('hello')</code> evaluates to
+<code>'o'</code>. This means that
+<code>sky.get('city').apply(max)</code> does actually run without error;
+it evaluates to a Series containing the last element in the name of each
+<code>'city'</code>.</p>
+<p>(This subpart was trickier than we intended – we ended up giving
+credit to both “error” and “Series”.)</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
@@ -3717,9 +3824,15 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-29.4">Problem 29.4</h3>
-<div class="sourceCode" id="cb48"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;floors&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
+<hr />
+<h2 id="problem-31">Problem 31</h2>
+<p>Below, identify the data type of the result of each of the following
+expressions, or select “error” if you believe the expression results in
+an error.</p>
+<p><br></p>
+<h3 id="problem-31.1">Problem 31.1</h3>
+<div class="sourceCode" id="cb49"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3731,34 +3844,35 @@ <h3 id="problem-29.4">Problem 29.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading29_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_4" aria-expanded="true" aria-controls="collapse29_4">
+<h2 class="accordion-header" id="heading31_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_1" aria-expanded="true" aria-controls="collapse31_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse29_4" class="accordion-collapse collapse"
-aria-labelledby="heading29_4" data-bs-parent="#accordionExample">
+<div id="collapse31_1" class="accordion-collapse collapse"
+aria-labelledby="heading31_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> int or float</p>
-<p>The Series <code>sky.get('floors')</code> is made up of integers, and
-<code>sky.get('floors').max()</code> evaluates to the largest number in
-the Series, which is also an integer.</p>
+<p><strong>Answer:</strong> DataFrame</p>
+<p><code>sky</code> is a DataFrame. All the <code>sort_values</code>
+method does is change the order of the rows in the Series/DataFrame it
+is called on, it does not change the data structure. As such,
+<code>sky.sort_values('height')</code> is also a DataFrame.</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 87%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-29.5">Problem 29.5</h3>
-<div class="sourceCode" id="cb49"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a>sky.groupby(<span class="st">&#39;material&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
+<h3 id="problem-31.2">Problem 31.2</h3>
+<div class="sourceCode" id="cb50"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb50-1"><a href="#cb50-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).loc[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3770,40 +3884,44 @@ <h3 id="problem-29.5">Problem 29.5</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading29_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_5" aria-expanded="true" aria-controls="collapse29_5">
+<h2 class="accordion-header" id="heading31_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_2" aria-expanded="true" aria-controls="collapse31_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse29_5" class="accordion-collapse collapse"
-aria-labelledby="heading29_5" data-bs-parent="#accordionExample">
+<div id="collapse31_2" class="accordion-collapse collapse"
+aria-labelledby="heading31_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> DataFrame</p>
-<p>When grouping and using an aggregation method, the result is always a
-DataFrame. The DataFrame <code>sky.groupby('material').max()</code>
-contains all of the columns in <code>sky</code>, minus
-<code>'material'</code>, which has been moved to the index. It contains
-one row for each unique <code>'material'</code>.</p>
-<p>Note that no columns were “dropped”, as may happen when using
-<code>.mean()</code>, because <code>.max()</code> can work on Series’ of
-any type. You can take the max of strings, while you cannot take the
-mean of strings.</p>
+<p><strong>Answer:</strong> error</p>
+<p><code>sky.sort_values('height')</code> is a DataFrame, and
+<code>sky.sort_values('height').get('material')</code> is a Series
+corresponding to the <code>'material'</code> column, sorted by
+<code>'height'</code> in increasing order. So far, there are no
+errors.</p>
+<p>Remember, the <code>.loc</code> <em>accessor</em> is used to access
+elements in a Series based on their index.
+<code>sky.sort_values('height').get('material').loc[0]</code> is asking
+for the element in the
+<code>sky.sort_values('height').get('material')</code> Series with index
+0. However, the index of <code>sky</code> is made up of building names.
+Since there is no building named <code>0</code>, <code>.loc[0]</code>
+causes an error.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 78%.</p>
+<p>The average score on this problem was 79%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-29.6">Problem 29.6</h3>
-<div class="sourceCode" id="cb50"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb50-1"><a href="#cb50-1" aria-hidden="true" tabindex="-1"></a>sky.index[<span class="dv">0</span>]</span></code></pre></div>
+<h3 id="problem-31.3">Problem 31.3</h3>
+<div class="sourceCode" id="cb51"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).iloc[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3815,42 +3933,83 @@ <h3 id="problem-29.6">Problem 29.6</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading29_6">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_6" aria-expanded="true" aria-controls="collapse29_6">
+<h2 class="accordion-header" id="heading31_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_3" aria-expanded="true" aria-controls="collapse31_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse29_6" class="accordion-collapse collapse"
-aria-labelledby="heading29_6" data-bs-parent="#accordionExample">
+<div id="collapse31_3" class="accordion-collapse collapse"
+aria-labelledby="heading31_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer:</strong> string</p>
-<p><code>sky.index</code> contains the values
-<code>'Bayard-Condict Building'</code>,
-<code>'The Yacht Club at Portofino'</code>,
-<code>'City Investing Building'</code>, etc. <code>sky.index[0]</code>
-is then <code>'Bayard-Condict Building'</code>, which is a string.</p>
+<p>As we mentioned above,
+<code>sky.sort_values('height').get('material')</code> is a Series
+containing values from the <code>'material'</code> column (but sorted).
+Remember, there is no element in this Series with an index of 0, so
+<code>sky.sort_values('height').get('material').loc[0]</code> errors.
+However, <code>.iloc[0]</code> works differently than
+<code>.loc[0]</code>; <code>.iloc[0]</code> will give us the first
+element in a Series (independent of what’s in the index). So,
+<code>sky.sort_values('height').get('material').iloc[0]</code> gives us
+back a value from the <code>'material'</code> column, which is made up
+of strings, so it gives us a string. (Specifically, it gives us the
+<code>'material'</code> type of the skyscraper with the smallest
+<code>'height'</code>.)</p>
 <hr/>
-<h5>Difficulty: ⭐️</h5>
+<h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 91%.</p>
+<p>The average score on this problem was 89%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<hr />
-<h2 id="problem-30">Problem 30</h2>
-<p>Below, identify the data type of the result of each of the following
-expressions, or select “error” if you believe the expression results in
-an error.</p>
+<h3 id="problem-31.4">Problem 31.4</h3>
+<div class="sourceCode" id="cb52"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;floors&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> int or float</p></li>
+<li><p><input type="radio" disabled="" /> Boolean</p></li>
+<li><p><input type="radio" disabled="" /> string</p></li>
+<li><p><input type="radio" disabled="" /> array</p></li>
+<li><p><input type="radio" disabled="" /> Series</p></li>
+<li><p><input type="radio" disabled="" /> DataFrame</p></li>
+<li><p><input type="radio" disabled="" /> error</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading31_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_4" aria-expanded="true" aria-controls="collapse31_4">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse31_4" class="accordion-collapse collapse"
+aria-labelledby="heading31_4" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> int or float</p>
+<p>The Series <code>sky.get('floors')</code> is made up of integers, and
+<code>sky.get('floors').max()</code> evaluates to the largest number in
+the Series, which is also an integer.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 91%.</p>
+</div>
+</div>
+</div>
+</div>
 <p><br></p>
-<h3 id="problem-30.1">Problem 30.1</h3>
-<div class="sourceCode" id="cb51"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">len</span>)</span></code></pre></div>
+<h3 id="problem-31.5">Problem 31.5</h3>
+<div class="sourceCode" id="cb53"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>sky.groupby(<span class="st">&#39;material&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3862,37 +4021,40 @@ <h3 id="problem-30.1">Problem 30.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading30_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_1" aria-expanded="true" aria-controls="collapse30_1">
+<h2 class="accordion-header" id="heading31_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_5" aria-expanded="true" aria-controls="collapse31_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse30_1" class="accordion-collapse collapse"
-aria-labelledby="heading30_1" data-bs-parent="#accordionExample">
+<div id="collapse31_5" class="accordion-collapse collapse"
+aria-labelledby="heading31_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> Series</p>
-<p>The <code>.apply</code> method takes in a function and evaluates that
-function on every element in a Series. Here,
-<code>sky.get('city').apply(len)</code> is using the function
-<code>len</code> on every element in the Series
-<code>sky.get('city')</code>. The result is also a Series, containing
-the lengths of the names of each <code>'city'</code>.</p>
+<p><strong>Answer:</strong> DataFrame</p>
+<p>When grouping and using an aggregation method, the result is always a
+DataFrame. The DataFrame <code>sky.groupby('material').max()</code>
+contains all of the columns in <code>sky</code>, minus
+<code>'material'</code>, which has been moved to the index. It contains
+one row for each unique <code>'material'</code>.</p>
+<p>Note that no columns were “dropped”, as may happen when using
+<code>.mean()</code>, because <code>.max()</code> can work on Series’ of
+any type. You can take the max of strings, while you cannot take the
+mean of strings.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 79%.</p>
+<p>The average score on this problem was 78%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-30.2">Problem 30.2</h3>
-<div class="sourceCode" id="cb52"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">max</span>)</span></code></pre></div>
+<h3 id="problem-31.6">Problem 31.6</h3>
+<div class="sourceCode" id="cb54"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>sky.index[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3904,61 +4066,42 @@ <h3 id="problem-30.2">Problem 30.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading30_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_2" aria-expanded="true" aria-controls="collapse30_2">
+<h2 class="accordion-header" id="heading31_6">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_6" aria-expanded="true" aria-controls="collapse31_6">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse30_2" class="accordion-collapse collapse"
-aria-labelledby="heading30_2" data-bs-parent="#accordionExample">
+<div id="collapse31_6" class="accordion-collapse collapse"
+aria-labelledby="heading31_6" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer:</strong> Series</p>
-<p>This is a tricky problem!</p>
-<p>The function that <code>apply</code> takes in must work on individual
-elements in a Series, i.e. it must work with just a single argument. We
-saw this in the above subpart, where
-<code>sky.get('city').apply(len)</code> applied <code>len</code> on each
-<code>'city'</code> name.</p>
-<p>Here, we are trying to apply the <code>max</code> function on each
-<code>'city'</code> name. The <code>max</code> of a single item does not
-work in Python, because taking the <code>max</code> requires comparing
-two or more elements. Try it out - in a notebook, run the expression
-<code>max(5)</code>, and you’ll see an error. So, if we tried to use
-<code>.apply(max)</code> on a Series of numbers, we’d run into an
-error.</p>
-<p><strong>However</strong>, we are using <code>.apply(max)</code> on a
-Series of strings, and it turns out that Python <strong>does</strong>
-allow us to take the <code>max</code> of a string! The <code>max</code>
-of a string in Python is defined as the last character in the string
-alphabetically, so <code>max('hello')</code> evaluates to
-<code>'o'</code>. This means that
-<code>sky.get('city').apply(max)</code> does actually run without error;
-it evaluates to a Series containing the last element in the name of each
-<code>'city'</code>.</p>
-<p>(This subpart was trickier than we intended – we ended up giving
-credit to both “error” and “Series”.)</p>
+<p><strong>Answer:</strong> string</p>
+<p><code>sky.index</code> contains the values
+<code>'Bayard-Condict Building'</code>,
+<code>'The Yacht Club at Portofino'</code>,
+<code>'City Investing Building'</code>, etc. <code>sky.index[0]</code>
+is then <code>'Bayard-Condict Building'</code>, which is a string.</p>
 <hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
+<h5>Difficulty: ⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 89%.</p>
+<p>The average score on this problem was 91%.</p>
 </div>
 </div>
 </div>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-31">Problem 31</h2>
+<h2 id="problem-32">Problem 32</h2>
 <p>Below, identify the data type of the result of each of the following
 expressions, or select “error” if you believe the expression results in
 an error.</p>
 <p><br></p>
-<h3 id="problem-31.1">Problem 31.1</h3>
-<div class="sourceCode" id="cb53"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>)</span></code></pre></div>
+<h3 id="problem-32.1">Problem 32.1</h3>
+<div class="sourceCode" id="cb55"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -3970,13 +4113,13 @@ <h3 id="problem-31.1">Problem 31.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_1" aria-expanded="true" aria-controls="collapse31_1">
+<h2 class="accordion-header" id="heading32_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_1" aria-expanded="true" aria-controls="collapse32_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_1" class="accordion-collapse collapse"
-aria-labelledby="heading31_1" data-bs-parent="#accordionExample">
+<div id="collapse32_1" class="accordion-collapse collapse"
+aria-labelledby="heading32_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3996,9 +4139,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.2">Problem 31.2</h3>
-<div class="sourceCode" id="cb54"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).loc[<span class="dv">0</span>]</span></code></pre></div>
+<h3 id="problem-32.2">Problem 32.2</h3>
+<div class="sourceCode" id="cb56"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).loc[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4010,13 +4153,13 @@ <h3 id="problem-31.2">Problem 31.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_2" aria-expanded="true" aria-controls="collapse31_2">
+<h2 class="accordion-header" id="heading32_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_2" aria-expanded="true" aria-controls="collapse32_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_2" class="accordion-collapse collapse"
-aria-labelledby="heading31_2" data-bs-parent="#accordionExample">
+<div id="collapse32_2" class="accordion-collapse collapse"
+aria-labelledby="heading32_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4045,9 +4188,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.3">Problem 31.3</h3>
-<div class="sourceCode" id="cb55"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).iloc[<span class="dv">0</span>]</span></code></pre></div>
+<h3 id="problem-32.3">Problem 32.3</h3>
+<div class="sourceCode" id="cb57"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>sky.sort_values(<span class="st">&#39;height&#39;</span>).get(<span class="st">&#39;material&#39;</span>).iloc[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4059,13 +4202,13 @@ <h3 id="problem-31.3">Problem 31.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_3" aria-expanded="true" aria-controls="collapse31_3">
+<h2 class="accordion-header" id="heading32_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_3" aria-expanded="true" aria-controls="collapse32_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_3" class="accordion-collapse collapse"
-aria-labelledby="heading31_3" data-bs-parent="#accordionExample">
+<div id="collapse32_3" class="accordion-collapse collapse"
+aria-labelledby="heading32_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4094,9 +4237,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.4">Problem 31.4</h3>
-<div class="sourceCode" id="cb56"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">len</span>)</span></code></pre></div>
+<h3 id="problem-32.4">Problem 32.4</h3>
+<div class="sourceCode" id="cb58"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">len</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4108,13 +4251,13 @@ <h3 id="problem-31.4">Problem 31.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_4" aria-expanded="true" aria-controls="collapse31_4">
+<h2 class="accordion-header" id="heading32_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_4" aria-expanded="true" aria-controls="collapse32_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_4" class="accordion-collapse collapse"
-aria-labelledby="heading31_4" data-bs-parent="#accordionExample">
+<div id="collapse32_4" class="accordion-collapse collapse"
+aria-labelledby="heading32_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4136,9 +4279,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.5">Problem 31.5</h3>
-<div class="sourceCode" id="cb57"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">max</span>)</span></code></pre></div>
+<h3 id="problem-32.5">Problem 32.5</h3>
+<div class="sourceCode" id="cb59"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb59-1"><a href="#cb59-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;city&#39;</span>).<span class="bu">apply</span>(<span class="bu">max</span>)</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4150,13 +4293,13 @@ <h3 id="problem-31.5">Problem 31.5</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_5" aria-expanded="true" aria-controls="collapse31_5">
+<h2 class="accordion-header" id="heading32_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_5" aria-expanded="true" aria-controls="collapse32_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_5" class="accordion-collapse collapse"
-aria-labelledby="heading31_5" data-bs-parent="#accordionExample">
+<div id="collapse32_5" class="accordion-collapse collapse"
+aria-labelledby="heading32_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4196,9 +4339,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.6">Problem 31.6</h3>
-<div class="sourceCode" id="cb58"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;floors&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
+<h3 id="problem-32.6">Problem 32.6</h3>
+<div class="sourceCode" id="cb60"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a>sky.get(<span class="st">&#39;floors&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4210,13 +4353,13 @@ <h3 id="problem-31.6">Problem 31.6</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_6">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_6" aria-expanded="true" aria-controls="collapse31_6">
+<h2 class="accordion-header" id="heading32_6">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_6" aria-expanded="true" aria-controls="collapse32_6">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_6" class="accordion-collapse collapse"
-aria-labelledby="heading31_6" data-bs-parent="#accordionExample">
+<div id="collapse32_6" class="accordion-collapse collapse"
+aria-labelledby="heading32_6" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4235,9 +4378,9 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.7">Problem 31.7</h3>
-<div class="sourceCode" id="cb59"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb59-1"><a href="#cb59-1" aria-hidden="true" tabindex="-1"></a>sky.groupby(<span class="st">&#39;material&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
+<h3 id="problem-32.7">Problem 32.7</h3>
+<div class="sourceCode" id="cb61"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a>sky.groupby(<span class="st">&#39;material&#39;</span>).<span class="bu">max</span>()</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4249,13 +4392,13 @@ <h3 id="problem-31.7">Problem 31.7</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_7">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_7" aria-expanded="true" aria-controls="collapse31_7">
+<h2 class="accordion-header" id="heading32_7">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_7" aria-expanded="true" aria-controls="collapse32_7">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_7" class="accordion-collapse collapse"
-aria-labelledby="heading31_7" data-bs-parent="#accordionExample">
+<div id="collapse32_7" class="accordion-collapse collapse"
+aria-labelledby="heading32_7" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4280,9 +4423,9 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.8">Problem 31.8</h3>
-<div class="sourceCode" id="cb60"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a>sky.index[<span class="dv">0</span>]</span></code></pre></div>
+<h3 id="problem-32.8">Problem 32.8</h3>
+<div class="sourceCode" id="cb62"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb62-1"><a href="#cb62-1" aria-hidden="true" tabindex="-1"></a>sky.index[<span class="dv">0</span>]</span></code></pre></div>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> int or float</p></li>
 <li><p><input type="radio" disabled="" /> Boolean</p></li>
@@ -4294,13 +4437,13 @@ <h3 id="problem-31.8">Problem 31.8</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_8">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_8" aria-expanded="true" aria-controls="collapse31_8">
+<h2 class="accordion-header" id="heading32_8">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32_8" aria-expanded="true" aria-controls="collapse32_8">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_8" class="accordion-collapse collapse"
-aria-labelledby="heading31_8" data-bs-parent="#accordionExample">
+<div id="collapse32_8" class="accordion-collapse collapse"
+aria-labelledby="heading32_8" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4322,73 +4465,27 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-32">Problem 32</h2>
-<p>In this question, we’ll write code to learn more about the
-skyscrapers in the beautiful city of San Diego. (Unrelated fun fact –
-since the San Diego Airport is so close to downtown, buildings in
-downtown San Diego legally cannot be taller than 152 meters.)</p>
-<p>Below, fill in the blank to create a DataFrame, named
-<code>san_tall</code>, consisting of just the skyscrapers in San Diego
-that are over 100 meters tall.</p>
-<div class="sourceCode" id="cb61"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a>condition <span class="op">=</span> ______</span>
-<span id="cb61-2"><a href="#cb61-2" aria-hidden="true" tabindex="-1"></a>san_tall <span class="op">=</span> sky[(sky.get(<span class="st">&#39;city&#39;</span>) <span class="op">==</span> <span class="st">&#39;San Diego&#39;</span>) <span class="op">&amp;</span> condition]</span></code></pre></div>
-<p>What goes in the blank?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading32">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse32" aria-expanded="true" aria-controls="collapse32">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse32" class="accordion-collapse collapse"
-aria-labelledby="heading32" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> <code>sky.get('height') &gt; 100</code></p>
-<p>We need to query for all of the skyscrapers that satisfy two
-conditions – the <code>'city'</code> must be <code>'San Diego'</code>
-and the <code>'height'</code> must be above 100. The first condition was
-already implemented for us, so we just need to construct a Boolean
-Series that implements the second condition.</p>
-<p>Here, we want all of the rows where <code>'height'</code> is above
-100, so we <code>get</code> the <code>'height'</code> column and compare
-it to 100 like so: <code>sky.get('height') &gt; 100</code>.</p>
-<hr/>
-<h5>Difficulty: ⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 95%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
 <h2 id="problem-33">Problem 33</h2>
 <p>In this question, we’ll write code to learn more about the
 skyscrapers in the beautiful city of San Diego. (Unrelated fun fact –
 since the San Diego Airport is so close to downtown, buildings in
 downtown San Diego legally cannot be taller than 152 meters.)</p>
-<p><br></p>
-<h3 id="problem-33.1">Problem 33.1</h3>
 <p>Below, fill in the blank to create a DataFrame, named
 <code>san_tall</code>, consisting of just the skyscrapers in San Diego
 that are over 100 meters tall.</p>
-<div class="sourceCode" id="cb62"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb62-1"><a href="#cb62-1" aria-hidden="true" tabindex="-1"></a>condition <span class="op">=</span> ______</span>
-<span id="cb62-2"><a href="#cb62-2" aria-hidden="true" tabindex="-1"></a>san_tall <span class="op">=</span> sky[(sky.get(<span class="st">&#39;city&#39;</span>) <span class="op">==</span> <span class="st">&#39;San Diego&#39;</span>) <span class="op">&amp;</span> condition]</span></code></pre></div>
+<div class="sourceCode" id="cb63"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a>condition <span class="op">=</span> ______</span>
+<span id="cb63-2"><a href="#cb63-2" aria-hidden="true" tabindex="-1"></a>san_tall <span class="op">=</span> sky[(sky.get(<span class="st">&#39;city&#39;</span>) <span class="op">==</span> <span class="st">&#39;San Diego&#39;</span>) <span class="op">&amp;</span> condition]</span></code></pre></div>
 <p>What goes in the blank?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading33_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_1" aria-expanded="true" aria-controls="collapse33_1">
+<h2 class="accordion-header" id="heading33">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33" aria-expanded="true" aria-controls="collapse33">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse33_1" class="accordion-collapse collapse"
-aria-labelledby="heading33_1" data-bs-parent="#accordionExample">
+<div id="collapse33" class="accordion-collapse collapse"
+aria-labelledby="heading33" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4411,103 +4508,6 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 </div>
-<p><br></p>
-<h3 id="problem-33.2">Problem 33.2</h3>
-<p>Suppose <code>san_tall</code> from the previous part was created
-correctly. Fill in the blanks so that <code>height_many_floors</code>
-evaluates to the <strong>height (in meters)</strong> of the skyscraper
-with the <strong>most floors</strong>, amongst all skyscrapers in San
-Diego that are over 100 meters tall.</p>
-<div class="sourceCode" id="cb63"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a>height_many_floors <span class="op">=</span> san_tall.______.iloc[<span class="dv">0</span>]</span></code></pre></div>
-<p>What goes in the blank?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading33_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_2" aria-expanded="true" aria-controls="collapse33_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse33_2" class="accordion-collapse collapse"
-aria-labelledby="heading33_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong>
-<code>sort_values('floors', ascending=False).get('height')</code></p>
-<p>The end of the line given to us is <code>.iloc[0]</code>. We know
-that <code>.iloc[0]</code> extracts the first element in whatever Series
-it is called on, so what comes before <code>.iloc[0]</code> must be a
-Series where the first element is the <code>'height'</code> of the
-skyscraper with the most floors, among all skyscrapers in San Diego that
-are over 100 meters tall. The DataFrame we are working with,
-<code>san_tall</code>, already only has skyscrapers in San Diego that
-are over 100 meters tall.</p>
-<p>This means that in the blank, all we need to do is:</p>
-<ol type="1">
-<li>Sort skyscrapers by <code>'floors'</code> in decreasing order (so
-that the first row is the skyscraper with the most
-<code>'floors'</code>).</li>
-<li>Extract the <code>'height'</code> column.</li>
-</ol>
-<p>As such, a complete answer is
-<code>height_many_floors = san_tall.sort_values('floors', ascending=False).get('height').iloc[0]</code>.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 74%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-33.3">Problem 33.3</h3>
-<p><code>height_many_floors</code>, the value you computed in the
-previous part (2.2) was a number.</p>
-<p><strong>True or False:</strong> Assuming that the DataFrame
-<code>san_tall</code> contains all skyscrapers in San Diego,
-<code>height_many_floors</code> is the height (in meters) of the
-<strong>tallest</strong> skyscraper in San Diego.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading33_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_3" aria-expanded="true" aria-controls="collapse33_3">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse33_3" class="accordion-collapse collapse"
-aria-labelledby="heading33_3" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> False</p>
-<p><code>height_many_floors</code> is the height of the skyscraper with
-the most <code>'floors'</code>. However, this is not necessarily the
-tallest skyscraper (i.e. the skyscraper with the largest
-<code>'height'</code>)! Consider the following scenario:</p>
-<ul>
-<li>Building A: 15 floors, height of 150 feet</li>
-<li>Building B: 20 floors, height of 100 feet</li>
-</ul>
-<p><code>height_many_floors</code> would be 100, but it is not the
-<code>'height'</code> of the taller building.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 84%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
 <hr />
 <p class="meta"><em>Source:</em> wi23-final — Q2</p>
 <h2 id="problem-34">Problem 34</h2>
diff --git a/docs/lectures/lec6/index.html b/docs/lectures/lec6/index.html
index d623fdb..dd559b7 100644
--- a/docs/lectures/lec6/index.html
+++ b/docs/lectures/lec6/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
 </head>
 <body>
 <header id="title-block-header">
diff --git a/docs/lectures/lec7/index.html b/docs/lectures/lec7/index.html
index 777cf1a..9c2d427 100644
--- a/docs/lectures/lec7/index.html
+++ b/docs/lectures/lec7/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -2808,6 +2808,44 @@ <h2 id="problem-19">Problem 19</h2>
 pint of store-brand ice cream.</p>
 <p><br></p>
 <h3 id="problem-19.1">Problem 19.1</h3>
+<p>What should <code>type(prices.get('broccoli').iloc[0])</code>
+output?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> int</p></li>
+<li><p><input type="radio" disabled="" /> float</p></li>
+<li><p><input type="radio" disabled="" /> array</p></li>
+<li><p><input type="radio" disabled="" /> Series</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading19_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_1" aria-expanded="true" aria-controls="collapse19_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse19_1" class="accordion-collapse collapse"
+aria-labelledby="heading19_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> float</p>
+<p>This code extracts the first entry of the <code>'broccoli'</code>
+column. Since this column contains prices in dollars for a pound of
+broccoli, it makes sense to represent such a price using a float,
+because the price of a pound of broccoli is not necessarily an
+integer.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 92%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-19.2">Problem 19.2</h3>
 <p>Using the code,</p>
 <div class="sourceCode" id="cb10"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>prices.plot(kind<span class="op">=</span><span class="st">&#39;hist&#39;</span>, y<span class="op">=</span><span class="st">&#39;broccoli&#39;</span>, bins<span class="op">=</span>np.arange(<span class="fl">0.8</span>, <span class="fl">2.11</span>, <span class="fl">0.1</span>), density<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
@@ -2818,13 +2856,13 @@ <h3 id="problem-19.1">Problem 19.1</h3>
 bar)?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading19_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_1" aria-expanded="true" aria-controls="collapse19_1">
+<h2 class="accordion-header" id="heading19_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_2" aria-expanded="true" aria-controls="collapse19_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse19_1" class="accordion-collapse collapse"
-aria-labelledby="heading19_1" data-bs-parent="#accordionExample">
+<div id="collapse19_2" class="accordion-collapse collapse"
+aria-labelledby="heading19_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2858,7 +2896,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-19.2">Problem 19.2</h3>
+<h3 id="problem-19.3">Problem 19.3</h3>
 <p>Suppose we now plot the same data with different bins, using the
 following line of code:</p>
 <div class="sourceCode" id="cb11"><pre
@@ -2868,13 +2906,13 @@ <h3 id="problem-19.2">Problem 19.2</h3>
 your answer below.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading19_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_2" aria-expanded="true" aria-controls="collapse19_2">
+<h2 class="accordion-header" id="heading19_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_3" aria-expanded="true" aria-controls="collapse19_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse19_2" class="accordion-collapse collapse"
-aria-labelledby="heading19_2" data-bs-parent="#accordionExample">
+<div id="collapse19_3" class="accordion-collapse collapse"
+aria-labelledby="heading19_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2927,7 +2965,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-19.3">Problem 19.3</h3>
+<h3 id="problem-19.4">Problem 19.4</h3>
 <p>You are interested in finding out the number of stores in which a
 pint of ice cream was cheaper than a pound of broccoli. Will you be able
 to determine the answer to this question by looking at the plot produced
@@ -2940,13 +2978,13 @@ <h3 id="problem-19.3">Problem 19.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading19_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_3" aria-expanded="true" aria-controls="collapse19_3">
+<h2 class="accordion-header" id="heading19_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_4" aria-expanded="true" aria-controls="collapse19_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse19_3" class="accordion-collapse collapse"
-aria-labelledby="heading19_3" data-bs-parent="#accordionExample">
+<div id="collapse19_4" class="accordion-collapse collapse"
+aria-labelledby="heading19_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -2978,7 +3016,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-19.4">Problem 19.4</h3>
+<h3 id="problem-19.5">Problem 19.5</h3>
 <p>You are interested in finding out the number of stores in which a
 pint of ice cream was cheaper than a pound of broccoli. Will you be able
 to determine the answer to this question by looking at the plot produced
@@ -2991,13 +3029,13 @@ <h3 id="problem-19.4">Problem 19.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading19_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_4" aria-expanded="true" aria-controls="collapse19_4">
+<h2 class="accordion-header" id="heading19_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_5" aria-expanded="true" aria-controls="collapse19_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse19_4" class="accordion-collapse collapse"
-aria-labelledby="heading19_4" data-bs-parent="#accordionExample">
+<div id="collapse19_5" class="accordion-collapse collapse"
+aria-labelledby="heading19_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3023,7 +3061,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-19.5">Problem 19.5</h3>
+<h3 id="problem-19.6">Problem 19.6</h3>
 <p>Some code and the scatterplot that produced it is shown below:</p>
 <div class="sourceCode" id="cb14"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>(prices.get([<span class="st">&#39;broccoli&#39;</span>, <span class="st">&#39;ice_cream&#39;</span>]).plot(kind<span class="op">=</span><span class="st">&#39;scatter&#39;</span>, x<span class="op">=</span><span class="st">&#39;broccoli&#39;</span>, y<span class="op">=</span><span class="st">&#39;ice_cream&#39;</span>))</span></code></pre></div>
@@ -3036,13 +3074,13 @@ <h3 id="problem-19.5">Problem 19.5</h3>
 question.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading19_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_5" aria-expanded="true" aria-controls="collapse19_5">
+<h2 class="accordion-header" id="heading19_6">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse19_6" aria-expanded="true" aria-controls="collapse19_6">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse19_5" class="accordion-collapse collapse"
-aria-labelledby="heading19_5" data-bs-parent="#accordionExample">
+<div id="collapse19_6" class="accordion-collapse collapse"
+aria-labelledby="heading19_6" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3125,44 +3163,6 @@ <h2 id="problem-21">Problem 21</h2>
 pint of store-brand ice cream.</p>
 <p><br></p>
 <h3 id="problem-21.1">Problem 21.1</h3>
-<p>What should <code>type(prices.get('broccoli').iloc[0])</code>
-output?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> int</p></li>
-<li><p><input type="radio" disabled="" /> float</p></li>
-<li><p><input type="radio" disabled="" /> array</p></li>
-<li><p><input type="radio" disabled="" /> Series</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading21_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_1" aria-expanded="true" aria-controls="collapse21_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse21_1" class="accordion-collapse collapse"
-aria-labelledby="heading21_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> float</p>
-<p>This code extracts the first entry of the <code>'broccoli'</code>
-column. Since this column contains prices in dollars for a pound of
-broccoli, it makes sense to represent such a price using a float,
-because the price of a pound of broccoli is not necessarily an
-integer.</p>
-<hr/>
-<h5>Difficulty: ⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 92%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-21.2">Problem 21.2</h3>
 <p>Using the code,</p>
 <div class="sourceCode" id="cb15"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>prices.plot(kind<span class="op">=</span><span class="st">&#39;hist&#39;</span>, y<span class="op">=</span><span class="st">&#39;broccoli&#39;</span>, bins<span class="op">=</span>np.arange(<span class="fl">0.8</span>, <span class="fl">2.11</span>, <span class="fl">0.1</span>), density<span class="op">=</span><span class="va">True</span>)</span></code></pre></div>
@@ -3173,13 +3173,13 @@ <h3 id="problem-21.2">Problem 21.2</h3>
 bar)?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_2" aria-expanded="true" aria-controls="collapse21_2">
+<h2 class="accordion-header" id="heading21_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_1" aria-expanded="true" aria-controls="collapse21_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_2" class="accordion-collapse collapse"
-aria-labelledby="heading21_2" data-bs-parent="#accordionExample">
+<div id="collapse21_1" class="accordion-collapse collapse"
+aria-labelledby="heading21_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3213,7 +3213,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-21.3">Problem 21.3</h3>
+<h3 id="problem-21.2">Problem 21.2</h3>
 <p>Suppose we now plot the same data with different bins, using the
 following line of code:</p>
 <div class="sourceCode" id="cb16"><pre
@@ -3223,13 +3223,13 @@ <h3 id="problem-21.3">Problem 21.3</h3>
 your answer below.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_3" aria-expanded="true" aria-controls="collapse21_3">
+<h2 class="accordion-header" id="heading21_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_2" aria-expanded="true" aria-controls="collapse21_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_3" class="accordion-collapse collapse"
-aria-labelledby="heading21_3" data-bs-parent="#accordionExample">
+<div id="collapse21_2" class="accordion-collapse collapse"
+aria-labelledby="heading21_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3282,7 +3282,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-21.4">Problem 21.4</h3>
+<h3 id="problem-21.3">Problem 21.3</h3>
 <p>You are interested in finding out the number of stores in which a
 pint of ice cream was cheaper than a pound of broccoli. Will you be able
 to determine the answer to this question by looking at the plot produced
@@ -3295,13 +3295,13 @@ <h3 id="problem-21.4">Problem 21.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_4" aria-expanded="true" aria-controls="collapse21_4">
+<h2 class="accordion-header" id="heading21_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_3" aria-expanded="true" aria-controls="collapse21_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_4" class="accordion-collapse collapse"
-aria-labelledby="heading21_4" data-bs-parent="#accordionExample">
+<div id="collapse21_3" class="accordion-collapse collapse"
+aria-labelledby="heading21_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3333,7 +3333,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-21.5">Problem 21.5</h3>
+<h3 id="problem-21.4">Problem 21.4</h3>
 <p>You are interested in finding out the number of stores in which a
 pint of ice cream was cheaper than a pound of broccoli. Will you be able
 to determine the answer to this question by looking at the plot produced
@@ -3346,13 +3346,13 @@ <h3 id="problem-21.5">Problem 21.5</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_5">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_5" aria-expanded="true" aria-controls="collapse21_5">
+<h2 class="accordion-header" id="heading21_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_4" aria-expanded="true" aria-controls="collapse21_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_5" class="accordion-collapse collapse"
-aria-labelledby="heading21_5" data-bs-parent="#accordionExample">
+<div id="collapse21_4" class="accordion-collapse collapse"
+aria-labelledby="heading21_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3378,7 +3378,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-21.6">Problem 21.6</h3>
+<h3 id="problem-21.5">Problem 21.5</h3>
 <p>Some code and the scatterplot that produced it is shown below:</p>
 <div class="sourceCode" id="cb19"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>(prices.get([<span class="st">&#39;broccoli&#39;</span>, <span class="st">&#39;ice_cream&#39;</span>]).plot(kind<span class="op">=</span><span class="st">&#39;scatter&#39;</span>, x<span class="op">=</span><span class="st">&#39;broccoli&#39;</span>, y<span class="op">=</span><span class="st">&#39;ice_cream&#39;</span>))</span></code></pre></div>
@@ -3391,13 +3391,13 @@ <h3 id="problem-21.6">Problem 21.6</h3>
 question.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading21_6">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_6" aria-expanded="true" aria-controls="collapse21_6">
+<h2 class="accordion-header" id="heading21_5">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse21_5" aria-expanded="true" aria-controls="collapse21_5">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse21_6" class="accordion-collapse collapse"
-aria-labelledby="heading21_6" data-bs-parent="#accordionExample">
+<div id="collapse21_5" class="accordion-collapse collapse"
+aria-labelledby="heading21_5" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3512,149 +3512,11 @@ <h5>Difficulty: ⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-23">Problem 23</h2>
-<p>Recall, the interval <span class="math inline">[a, b)</span> refers
-to numbers greater than or equal to <span class="math inline">a</span>
-and less than <span class="math inline">b</span>, and the interval <span
-class="math inline">[a, b]</span> refers to numbers greater than or
-equal to <span class="math inline">a</span> and less than or equal to
-<span class="math inline">b</span>.</p>
-<p>Suppose we created a DataFrame, <code>medium_sky</code>, containing
-only the skyscrapers in <code>sky</code> whose number of floors are in
-the interval <span class="math inline">[20, 60]</span>. Below, we’ve
-drawn a histogram of the number of floors of all skyscrapers in
-<code>medium_sky</code>.</p>
-<center><img src='../../assets/images/wi22-midterm/floors-hist.png' width=40%></center>
-<p><br></p>
-<h3 id="problem-23.1">Problem 23.1</h3>
-<p>Suppose that there are 160 skyscrapers whose number of floors are in
-the interval <span class="math inline">[30, 35)</span>.</p>
-<p>Given this information and the histogram above, how many skyscrapers
-are there in <code>medium_sky</code>?</p>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading23_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse23_1" aria-expanded="true" aria-controls="collapse23_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse23_1" class="accordion-collapse collapse"
-aria-labelledby="heading23_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> 800</p>
-<p>Recall, in a histogram,</p>
-<p><span class="math display">\text{proportion of values in bin} =
-\text{area of bar} = \text{width of bin} \cdot \text{height of
-bar}</span></p>
-<p>Also, note that:</p>
-<p><span class="math display">\text{\# of values satisfying condition} =
-\text{proportion of values satisfying condition} \cdot \text{total \# of
-values}</span></p>
-<p>Here, we’re given the entire histogram, so we can find the proportion
-of values in the <span class="math inline">[30, 35)</span> bin. We are
-also given the number of values in the <span class="math inline">[30,
-35)</span> bin (160). This means we can use the second equation above to
-find the total number of skyscrapers in <code>medium_sky</code>.</p>
-<p>The first step is finding the area of the <span class="math inline">[30, 35)</span> bin’s bar. Its width is <span class="math inline">35-30 = 5</span>, and its height is <span class="math inline">0.04</span>, so its area is <span class="math inline">5 \cdot 0.04 = 0.2</span>. Then,</p>
-<p><span class="math display">\begin{aligned}
-        \text{\# of values satisfying condition} &amp;= \text{proportion
-of values satisfying condition} \cdot \text{total \# of values} \\
-        160 &amp;= 0.2 \cdot \text{total \# of values} \\
-        \implies \text{total \# of values} &amp;= \frac{160}{0.2} = 160
-\cdot 5 = 800
-\end{aligned}</span></p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 62%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-23.2">Problem 23.2</h3>
-<p>Again, suppose that there are 160 skyscrapers whose number of floors
-are in the interval <span class="math inline">[30, 35)</span>.</p>
-<p>Now suppose that there is a typo in the <code>medium_sky</code>
-DataFrame, and 20 skyscrapers were accidentally listed as having 53
-floors each when instead they actually only have 35 floors each. The
-histogram drawn above contains the incorrect version of the data.</p>
-<p>Suppose we re-draw the above histogram using the correct data. What
-will be the new heights of both the <span class="math inline">[35,
-40)</span> bar and <span class="math inline">[50, 55)</span> bar? Select
-the closest answer.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
-0.0325, and the <span class="math inline">[50, 55)</span> bar’s height
-becomes 0.0105.</p></li>
-<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
-0.035, and the <span class="math inline">[50, 55)</span> bar’s height
-becomes 0.008.</p></li>
-<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
-0.0375, and the <span class="math inline">[50, 55)</span> bar’s height
-becomes 0.0055.</p></li>
-<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
-0.04, and the <span class="math inline">[50, 55)</span> bar’s height
-becomes 0.003.</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading23_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse23_2" aria-expanded="true" aria-controls="collapse23_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse23_2" class="accordion-collapse collapse"
-aria-labelledby="heading23_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong> The <span class="math inline">[35,
-40)</span> bar’s height becomes 0.035, and the <span class="math inline">[50, 55)</span> bar’s height becomes 0.008.</p>
-<p>The current height of the <span class="math inline">[35, 40)</span>
-bar is 0.03, and the current height of the <span class="math inline">[50, 55)</span> bar is 0.013 (approximately; its
-height appears to be slightly more than halfway between 0.01 and 0.015).
-We need to decrease the height of the <span class="math inline">[50,
-55)</span> bar and increase the height of the <span class="math inline">[35, 40)</span> bar. The combined area of both bars
-must stay the same, since the proportion of values in their bins
-(together) is not changing. This means that the amount we need to
-decrease the <span class="math inline">[50, 55)</span> bar’s height by
-is the same as the amount we need to increase the <span class="math inline">[35, 40)</span> bar’s height by. Note that this
-relationship is true in all 4 answer choices.</p>
-<p>In the question, we were told that 20 skyscrapers were incorrectly
-binned. There are 800 skyscrapers total, so the proportion of
-skyscrapers that were incorrectly binned is <span class="math inline">\frac{20}{800} = 0.025</span>. This means that the
-area of the <span class="math inline">[35, 40)</span> bar needs to
-increase by 0.025 and the area of the <span class="math inline">[50,
-55)</span> bar needs to decrease by 0.025. Recall, each bar has width 5.
-That means that the “rectangular section” we will add to the <span class="math inline">[35, 40)</span> bar and remove from the <span class="math inline">[50, 55)</span> bar has height</p>
-<p><span class="math display">\text{height} =
-\frac{\text{area}}{\text{width}} = \frac{0.025}{5} = 0.005</span></p>
-<p>Thus, the height of the <span class="math inline">[35, 40)</span> bar
-becomes <span class="math inline">0.03 + 0.005 = 0.035</span> and the
-height of the <span class="math inline">[50, 55)</span> bar becomes
-<span class="math inline">0.013 - 0.005 = 0.008</span>.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 74%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
-<h2 id="problem-24">Problem 24</h2>
 <p>Consider the following line plot, which depicts the number of
 skyscrapers built per year.</p>
 <center><img src='../../assets/images/wi22-midterm/sky-per-year.png' width=40%></center>
 <p><br></p>
-<h3 id="problem-24.1">Problem 24.1</h3>
+<h3 id="problem-23.1">Problem 23.1</h3>
 <p>We created the line plot above using the following line of code:</p>
 <div class="sourceCode" id="cb20"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>sky.groupby(<span class="st">&#39;year&#39;</span>).count().plot(kind<span class="op">=</span><span class="st">&#39;line&#39;</span>, y<span class="op">=</span><span class="st">&#39;height&#39;</span>)<span class="op">;</span></span></code></pre></div>
@@ -3671,13 +3533,13 @@ <h3 id="problem-24.1">Problem 24.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading24_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse24_1" aria-expanded="true" aria-controls="collapse24_1">
+<h2 class="accordion-header" id="heading23_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse23_1" aria-expanded="true" aria-controls="collapse23_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse24_1" class="accordion-collapse collapse"
-aria-labelledby="heading24_1" data-bs-parent="#accordionExample">
+<div id="collapse23_1" class="accordion-collapse collapse"
+aria-labelledby="heading23_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3707,7 +3569,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-24.2">Problem 24.2</h3>
+<h3 id="problem-23.2">Problem 23.2</h3>
 <p><span style="color:red"><b>Note: This problem is out of scope; it
 covers material no longer included in the course.</b></span></p>
 <p>Now let’s look at the number of skyscrapers built each year since
@@ -3730,13 +3592,13 @@ <h3 id="problem-24.2">Problem 24.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading24_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse24_2" aria-expanded="true" aria-controls="collapse24_2">
+<h2 class="accordion-header" id="heading23_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse23_2" aria-expanded="true" aria-controls="collapse23_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse24_2" class="accordion-collapse collapse"
-aria-labelledby="heading24_2" data-bs-parent="#accordionExample">
+<div id="collapse23_2" class="accordion-collapse collapse"
+aria-labelledby="heading23_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3776,7 +3638,7 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-24.3">Problem 24.3</h3>
+<h3 id="problem-23.3">Problem 23.3</h3>
 <p>In which of the following scenarios would it make sense to draw a
 overlaid histogram?</p>
 <ul class="task-list">
@@ -3791,13 +3653,13 @@ <h3 id="problem-24.3">Problem 24.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading24_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse24_3" aria-expanded="true" aria-controls="collapse24_3">
+<h2 class="accordion-header" id="heading23_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse23_3" aria-expanded="true" aria-controls="collapse23_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse24_3" class="accordion-collapse collapse"
-aria-labelledby="heading24_3" data-bs-parent="#accordionExample">
+<div id="collapse23_3" class="accordion-collapse collapse"
+aria-labelledby="heading23_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -3840,6 +3702,144 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-24">Problem 24</h2>
+<p>Recall, the interval <span class="math inline">[a, b)</span> refers
+to numbers greater than or equal to <span class="math inline">a</span>
+and less than <span class="math inline">b</span>, and the interval <span
+class="math inline">[a, b]</span> refers to numbers greater than or
+equal to <span class="math inline">a</span> and less than or equal to
+<span class="math inline">b</span>.</p>
+<p>Suppose we created a DataFrame, <code>medium_sky</code>, containing
+only the skyscrapers in <code>sky</code> whose number of floors are in
+the interval <span class="math inline">[20, 60]</span>. Below, we’ve
+drawn a histogram of the number of floors of all skyscrapers in
+<code>medium_sky</code>.</p>
+<center><img src='../../assets/images/wi22-midterm/floors-hist.png' width=40%></center>
+<p><br></p>
+<h3 id="problem-24.1">Problem 24.1</h3>
+<p>Suppose that there are 160 skyscrapers whose number of floors are in
+the interval <span class="math inline">[30, 35)</span>.</p>
+<p>Given this information and the histogram above, how many skyscrapers
+are there in <code>medium_sky</code>?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading24_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse24_1" aria-expanded="true" aria-controls="collapse24_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse24_1" class="accordion-collapse collapse"
+aria-labelledby="heading24_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> 800</p>
+<p>Recall, in a histogram,</p>
+<p><span class="math display">\text{proportion of values in bin} =
+\text{area of bar} = \text{width of bin} \cdot \text{height of
+bar}</span></p>
+<p>Also, note that:</p>
+<p><span class="math display">\text{\# of values satisfying condition} =
+\text{proportion of values satisfying condition} \cdot \text{total \# of
+values}</span></p>
+<p>Here, we’re given the entire histogram, so we can find the proportion
+of values in the <span class="math inline">[30, 35)</span> bin. We are
+also given the number of values in the <span class="math inline">[30,
+35)</span> bin (160). This means we can use the second equation above to
+find the total number of skyscrapers in <code>medium_sky</code>.</p>
+<p>The first step is finding the area of the <span class="math inline">[30, 35)</span> bin’s bar. Its width is <span class="math inline">35-30 = 5</span>, and its height is <span class="math inline">0.04</span>, so its area is <span class="math inline">5 \cdot 0.04 = 0.2</span>. Then,</p>
+<p><span class="math display">\begin{aligned}
+        \text{\# of values satisfying condition} &amp;= \text{proportion
+of values satisfying condition} \cdot \text{total \# of values} \\
+        160 &amp;= 0.2 \cdot \text{total \# of values} \\
+        \implies \text{total \# of values} &amp;= \frac{160}{0.2} = 160
+\cdot 5 = 800
+\end{aligned}</span></p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 62%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-24.2">Problem 24.2</h3>
+<p>Again, suppose that there are 160 skyscrapers whose number of floors
+are in the interval <span class="math inline">[30, 35)</span>.</p>
+<p>Now suppose that there is a typo in the <code>medium_sky</code>
+DataFrame, and 20 skyscrapers were accidentally listed as having 53
+floors each when instead they actually only have 35 floors each. The
+histogram drawn above contains the incorrect version of the data.</p>
+<p>Suppose we re-draw the above histogram using the correct data. What
+will be the new heights of both the <span class="math inline">[35,
+40)</span> bar and <span class="math inline">[50, 55)</span> bar? Select
+the closest answer.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
+0.0325, and the <span class="math inline">[50, 55)</span> bar’s height
+becomes 0.0105.</p></li>
+<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
+0.035, and the <span class="math inline">[50, 55)</span> bar’s height
+becomes 0.008.</p></li>
+<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
+0.0375, and the <span class="math inline">[50, 55)</span> bar’s height
+becomes 0.0055.</p></li>
+<li><p><input type="radio" disabled="" /> The <span class="math inline">[35, 40)</span> bar’s height becomes
+0.04, and the <span class="math inline">[50, 55)</span> bar’s height
+becomes 0.003.</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading24_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse24_2" aria-expanded="true" aria-controls="collapse24_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse24_2" class="accordion-collapse collapse"
+aria-labelledby="heading24_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong> The <span class="math inline">[35,
+40)</span> bar’s height becomes 0.035, and the <span class="math inline">[50, 55)</span> bar’s height becomes 0.008.</p>
+<p>The current height of the <span class="math inline">[35, 40)</span>
+bar is 0.03, and the current height of the <span class="math inline">[50, 55)</span> bar is 0.013 (approximately; its
+height appears to be slightly more than halfway between 0.01 and 0.015).
+We need to decrease the height of the <span class="math inline">[50,
+55)</span> bar and increase the height of the <span class="math inline">[35, 40)</span> bar. The combined area of both bars
+must stay the same, since the proportion of values in their bins
+(together) is not changing. This means that the amount we need to
+decrease the <span class="math inline">[50, 55)</span> bar’s height by
+is the same as the amount we need to increase the <span class="math inline">[35, 40)</span> bar’s height by. Note that this
+relationship is true in all 4 answer choices.</p>
+<p>In the question, we were told that 20 skyscrapers were incorrectly
+binned. There are 800 skyscrapers total, so the proportion of
+skyscrapers that were incorrectly binned is <span class="math inline">\frac{20}{800} = 0.025</span>. This means that the
+area of the <span class="math inline">[35, 40)</span> bar needs to
+increase by 0.025 and the area of the <span class="math inline">[50,
+55)</span> bar needs to decrease by 0.025. Recall, each bar has width 5.
+That means that the “rectangular section” we will add to the <span class="math inline">[35, 40)</span> bar and remove from the <span class="math inline">[50, 55)</span> bar has height</p>
+<p><span class="math display">\text{height} =
+\frac{\text{area}}{\text{width}} = \frac{0.025}{5} = 0.005</span></p>
+<p>Thus, the height of the <span class="math inline">[35, 40)</span> bar
+becomes <span class="math inline">0.03 + 0.005 = 0.035</span> and the
+height of the <span class="math inline">[50, 55)</span> bar becomes
+<span class="math inline">0.013 - 0.005 = 0.008</span>.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 74%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
 <p class="meta"><em>Source:</em> wi24-final — Q16</p>
 <h2 id="problem-25">Problem 25</h2>
 <p>Suppose <code>males</code> is a DataFrame of all male Olympic
diff --git a/docs/lectures/lec8/index.html b/docs/lectures/lec8/index.html
index 2614a08..ff075f7 100644
--- a/docs/lectures/lec8/index.html
+++ b/docs/lectures/lec8/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
 </head>
 <body>
 <header id="title-block-header">
@@ -1078,152 +1078,97 @@ <h5>Difficulty:
 <p><br></p>
 <hr />
 <h2 id="problem-9">Problem 9</h2>
-<p>In the <code>ikea</code> DataFrame, the first word of each string in
-the <code>'product'</code> column represents the product line. For
-example the HEMNES line of products includes several different products,
-such as beds, dressers, and bedside tables.</p>
-<p>The code below assigns a new column to the <code>ikea</code>
-DataFrame containing the product line associated with each product.</p>
+<p>Complete the implementation of the <code>to_minutes</code> function
+below. This function takes as input a string formatted as
+<code>'x hr, y min'</code> where <code>x</code> and <code>y</code>
+represent integers, and returns the corresponding number of minutes,
+<strong>as an integer</strong> (type <code>int</code> in Python).</p>
+<p>For example, <code>to_minutes('3 hr, 5 min')</code> should return
+185.</p>
 <div class="sourceCode" id="cb13"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>(ikea.assign(product_line <span class="op">=</span> ikea.get(<span class="st">&#39;product&#39;</span>)</span>
-<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>                                .<span class="bu">apply</span>(extract_product_line)))</span></code></pre></div>
-<p><br></p>
-<h3 id="problem-9.1">Problem 9.1</h3>
-<p>What are the input and output types of the
-<code>extract_product_line</code> function?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> takes a string as input, returns a string</p></li>
-<li><p><input type="radio" disabled="" /> takes a string as input, returns a Series</p></li>
-<li><p><input type="radio" disabled="" /> takes a Series as input, returns a string</p></li>
-<li><p><input type="radio" disabled="" /> takes a Series as input, returns a Series</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading9_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_1" aria-expanded="true" aria-controls="collapse9_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse9_1" class="accordion-collapse collapse"
-aria-labelledby="heading9_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> takes a string as input, returns a
-string</p>
-<p>To use the Series method <code>.apply</code>, we first need a Series,
-containing values of any type. We pass in the name of a function to
-<code>.apply</code> and essentially, <code>.apply</code> calls the given
-function on each value of the Series, producing a Series with the
-resulting outputs of those function calls. In this case,
-<code>.apply(extract_product_line)</code> is called on the Series
-<code>ikea.get('product')</code>, which contains string values. This
-means the function <code>extract_product_line</code> must take strings
-as inputs. We’re told that the code assigns a new column to the
-<code>ikea</code> DataFrame containing the product line associated with
-each product, and we know that the product line is a string, as it’s the
-first word of the product name. This means the function
-<code>extract_product_line</code> must output a string.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 72%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-9.2">Problem 9.2</h3>
-<p>Complete the return statement in the
-<code>extract_product_line</code> function below.</p>
-<div class="sourceCode" id="cb14"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> extract_product_line(x):</span>
-<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
+class="sourceCode py"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> to_minutes(time):</span>
+<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>    first_split <span class="op">=</span> time.split(<span class="st">&#39; hr, &#39;</span>)</span>
+<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>    second_split <span class="op">=</span> first_split[<span class="dv">1</span>].split(<span class="st">&#39; min&#39;</span>)</span>
+<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
 <p>What goes in the blank?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading9_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9_2" aria-expanded="true" aria-controls="collapse9_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse9_2" class="accordion-collapse collapse"
-aria-labelledby="heading9_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> <code>x.split(' ')[0]</code></p>
-<p>This function should take as input a string <code>x</code>,
-representing a product name, and return the first word of that string,
-representing the product line. Since words are separated by spaces, we
-want to split the string on the space character <code>' '</code>.</p>
-<p>It’s also correct to answer <code>x.split()[0]</code> without
-specifying to split on spaces, because the default behavior of the
-string <code>.split</code> method is to split on any whitespace, which
-includes any number of spaces, tabs, newlines, etc. Since we’re only
-extracting the first word, which will be separated from the rest of the
-product name by a single space, it’s equivalent to split using single
-spaces and using the default of any whitespace. </p>
-<hr/>
-<h5>Difficulty:
-⭐️⭐️</h5>
-<p>The average score on this problem was 84%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
-<h2 id="problem-10">Problem 10</h2>
-<p>Suppose that when someone downloads the app, the app requires them to
-choose a username, which must be different from all other registered
-usernames.</p>
-<p><strong>True or False</strong>: If <code>app_data</code> had included
-a column with the username of the person who reported each product
-build, it would make sense to index <code>app_data</code> by
-username.</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> True</p></li>
-<li><p><input type="radio" disabled="" /> False</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading10">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10" aria-expanded="true" aria-controls="collapse10">
+<h2 class="accordion-header" id="heading9">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse9" aria-expanded="true" aria-controls="collapse9">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse10" class="accordion-collapse collapse"
-aria-labelledby="heading10" data-bs-parent="#accordionExample">
+<div id="collapse9" class="accordion-collapse collapse"
+aria-labelledby="heading9" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong> False</p>
-<p>Even though people must have distinct usernames, one person can build
-multiple different IKEA products and log their time for each build. So
-we don’t expect every row of <code>app_data</code> to have a distinct
-username associated with it, and therefore username would not be
-suitable as an index, since the index should have distinct values.</p>
+<p><strong>Answer: </strong>
+<code>int(first_split[0])*60+int(second_split[0])</code></p>
+<p>As the last subpart demonstrated, if we want to compare times, it
+doesn’t make sense to do so when times are represented as strings. In
+the <code>to_minutes</code> function, we convert a time string into an
+integer number of minutes.</p>
+<p>The first step is to understand the logic. Every hour contains 60
+minutes, so for a time string formatted like <code>x hr, y min'</code>
+the total number of minutes comes from multiplying the value of
+<code>x</code> by 60 and adding <code>y</code>.</p>
+<p>The second step is to understand how to extract the <code>x</code>
+and <code>y</code> values from the time string using the string methods
+<code>.split</code>. The string method <code>.split</code> takes as
+input some separator string and breaks the string into pieces at each
+instance of the separator string. It then returns a list of all those
+pieces. The first line of code, therefore, creates a list called
+<code>first_split</code> containing two elements. The first element,
+accessed by <code>first_split[0]</code> contains the part of the time
+string that comes before <code>' hr, '</code>. That is,
+<code>first_split[0]</code> evaluates to the string <code>x</code>.</p>
+<p>Similarly, <code>first_split[1]</code> contains the part of the time
+string that comes after <code>' hr, '</code>. So it is formatted like
+<code>'y min'</code>. If we split this string again using the separator
+of <code>' min'</code>, the result will be a list whose first element is
+the string <code>'y'</code>. This list is saved as
+<code>second_split</code> so <code>second_split[0]</code> evaluates to
+the string <code>y</code>.</p>
+<p>Now we have the pieces we need to compute the number of minutes,
+using the idea of multiplying the value of <code>x</code> by 60 and
+adding <code>y</code>. We have to be careful with data types here, as
+the bolded instructions warn us that the function must return an
+integer. Right now, <code>first_split[0]</code> evaluates to the string
+<code>x</code> and <code>second_split[0]</code> evaluates to the string
+<code>y</code>. We need to convert these strings to integers before we
+can multiply and add. Once we convert using the <code>int</code>
+function, then we can multiply the number of hours by 60 and add the
+number of minutes. Therefore, the solution is
+<code>int(first_split[0])*60+int(second_split[0])</code>.</p>
+<p>Note that failure to convert strings to integers using the
+<code>int</code> function would lead to very different behavior. Let’s
+take the example time string of <code>'3 hr, 5 min'</code> as input to
+our function. With the return statement as
+<code>int(first_split[0])*60+int(second_split[0])</code>, the function
+would return 185 on this input, as desired. With the return statement as
+<code>first_split[0]*60+second_split[0]</code>, the function would
+return a string of length 61, looking something like this
+<code>'3333...33335'</code>. That’s because the <code>*</code> and
+<code>+</code> symbols do have meaning for strings, they’re just
+different meanings than when used with integers.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 52%.</p>
+<p>The average score on this problem was 71%.</p>
 </div>
 </div>
 </div>
 </div>
 <hr />
-<h2 id="problem-11">Problem 11</h2>
+<h2 id="problem-10">Problem 10</h2>
 <p>Recall that an IKEA fan created an app for people to log the amount
 of time it takes them to assemble an IKEA product. We have this data in
 <code>app_data</code>.</p>
 <p><br></p>
-<h3 id="problem-11.1">Problem 11.1</h3>
+<h3 id="problem-10.1">Problem 10.1</h3>
 <p>Suppose that when someone downloads the app, the app requires them to
 choose a username, which must be different from all other registered
 usernames.</p>
@@ -1237,13 +1182,13 @@ <h3 id="problem-11.1">Problem 11.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_1" aria-expanded="true" aria-controls="collapse11_1">
+<h2 class="accordion-header" id="heading10_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_1" aria-expanded="true" aria-controls="collapse10_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_1" class="accordion-collapse collapse"
-aria-labelledby="heading11_1" data-bs-parent="#accordionExample">
+<div id="collapse10_1" class="accordion-collapse collapse"
+aria-labelledby="heading10_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1264,24 +1209,24 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-11.2">Problem 11.2</h3>
+<h3 id="problem-10.2">Problem 10.2</h3>
 <p>What does the code below evaluate to?</p>
-<div class="sourceCode" id="cb15"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>(app_data.take(np.arange(<span class="dv">4</span>))</span>
-<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>         .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_time&#39;</span>)</span>
-<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>         .get(<span class="st">&#39;assembly_time&#39;</span>)</span>
-<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a>         .iloc[<span class="dv">0</span>])</span></code></pre></div>
+<div class="sourceCode" id="cb14"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>(app_data.take(np.arange(<span class="dv">4</span>))</span>
+<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>         .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_time&#39;</span>)</span>
+<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a>         .get(<span class="st">&#39;assembly_time&#39;</span>)</span>
+<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>         .iloc[<span class="dv">0</span>])</span></code></pre></div>
 <p><em>Hint:</em> The <code>'assembly_time'</code> column contains
 strings.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading11_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11_2" aria-expanded="true" aria-controls="collapse11_2">
+<h2 class="accordion-header" id="heading10_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse10_2" aria-expanded="true" aria-controls="collapse10_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse11_2" class="accordion-collapse collapse"
-aria-labelledby="heading11_2" data-bs-parent="#accordionExample">
+<div id="collapse10_2" class="accordion-collapse collapse"
+aria-labelledby="heading10_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1314,98 +1259,53 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-12">Problem 12</h2>
-<p>Complete the implementation of the <code>to_minutes</code> function
-below. This function takes as input a string formatted as
-<code>'x hr, y min'</code> where <code>x</code> and <code>y</code>
-represent integers, and returns the corresponding number of minutes,
-<strong>as an integer</strong> (type <code>int</code> in Python).</p>
-<p>For example, <code>to_minutes('3 hr, 5 min')</code> should return
-185.</p>
-<div class="sourceCode" id="cb16"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> to_minutes(time):</span>
-<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>    first_split <span class="op">=</span> time.split(<span class="st">&#39; hr, &#39;</span>)</span>
-<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a>    second_split <span class="op">=</span> first_split[<span class="dv">1</span>].split(<span class="st">&#39; min&#39;</span>)</span>
-<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
-<p>What goes in the blank?</p>
+<h2 id="problem-11">Problem 11</h2>
+<p>Suppose that when someone downloads the app, the app requires them to
+choose a username, which must be different from all other registered
+usernames.</p>
+<p><strong>True or False</strong>: If <code>app_data</code> had included
+a column with the username of the person who reported each product
+build, it would make sense to index <code>app_data</code> by
+username.</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> True</p></li>
+<li><p><input type="radio" disabled="" /> False</p></li>
+</ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading12">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12" aria-expanded="true" aria-controls="collapse12">
+<h2 class="accordion-header" id="heading11">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse11" aria-expanded="true" aria-controls="collapse11">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse12" class="accordion-collapse collapse"
-aria-labelledby="heading12" data-bs-parent="#accordionExample">
+<div id="collapse11" class="accordion-collapse collapse"
+aria-labelledby="heading11" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
-<p><strong>Answer: </strong>
-<code>int(first_split[0])*60+int(second_split[0])</code></p>
-<p>As the last subpart demonstrated, if we want to compare times, it
-doesn’t make sense to do so when times are represented as strings. In
-the <code>to_minutes</code> function, we convert a time string into an
-integer number of minutes.</p>
-<p>The first step is to understand the logic. Every hour contains 60
-minutes, so for a time string formatted like <code>x hr, y min'</code>
-the total number of minutes comes from multiplying the value of
-<code>x</code> by 60 and adding <code>y</code>.</p>
-<p>The second step is to understand how to extract the <code>x</code>
-and <code>y</code> values from the time string using the string methods
-<code>.split</code>. The string method <code>.split</code> takes as
-input some separator string and breaks the string into pieces at each
-instance of the separator string. It then returns a list of all those
-pieces. The first line of code, therefore, creates a list called
-<code>first_split</code> containing two elements. The first element,
-accessed by <code>first_split[0]</code> contains the part of the time
-string that comes before <code>' hr, '</code>. That is,
-<code>first_split[0]</code> evaluates to the string <code>x</code>.</p>
-<p>Similarly, <code>first_split[1]</code> contains the part of the time
-string that comes after <code>' hr, '</code>. So it is formatted like
-<code>'y min'</code>. If we split this string again using the separator
-of <code>' min'</code>, the result will be a list whose first element is
-the string <code>'y'</code>. This list is saved as
-<code>second_split</code> so <code>second_split[0]</code> evaluates to
-the string <code>y</code>.</p>
-<p>Now we have the pieces we need to compute the number of minutes,
-using the idea of multiplying the value of <code>x</code> by 60 and
-adding <code>y</code>. We have to be careful with data types here, as
-the bolded instructions warn us that the function must return an
-integer. Right now, <code>first_split[0]</code> evaluates to the string
-<code>x</code> and <code>second_split[0]</code> evaluates to the string
-<code>y</code>. We need to convert these strings to integers before we
-can multiply and add. Once we convert using the <code>int</code>
-function, then we can multiply the number of hours by 60 and add the
-number of minutes. Therefore, the solution is
-<code>int(first_split[0])*60+int(second_split[0])</code>.</p>
-<p>Note that failure to convert strings to integers using the
-<code>int</code> function would lead to very different behavior. Let’s
-take the example time string of <code>'3 hr, 5 min'</code> as input to
-our function. With the return statement as
-<code>int(first_split[0])*60+int(second_split[0])</code>, the function
-would return 185 on this input, as desired. With the return statement as
-<code>first_split[0]*60+second_split[0]</code>, the function would
-return a string of length 61, looking something like this
-<code>'3333...33335'</code>. That’s because the <code>*</code> and
-<code>+</code> symbols do have meaning for strings, they’re just
-different meanings than when used with integers.</p>
+<p><strong>Answer: </strong> False</p>
+<p>Even though people must have distinct usernames, one person can build
+multiple different IKEA products and log their time for each build. So
+we don’t expect every row of <code>app_data</code> to have a distinct
+username associated with it, and therefore username would not be
+suitable as an index, since the index should have distinct values.</p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p>
 </p>
-<p>The average score on this problem was 71%.</p>
+<p>The average score on this problem was 52%.</p>
 </div>
 </div>
 </div>
 </div>
 <hr />
-<h2 id="problem-13">Problem 13</h2>
+<h2 id="problem-12">Problem 12</h2>
 <p>Recall that an IKEA fan created an app for people to log the amount
 of time it takes them to assemble an IKEA product. We have this data in
 <code>app_data</code>.</p>
 <p><br></p>
-<h3 id="problem-13.1">Problem 13.1</h3>
+<h3 id="problem-12.1">Problem 12.1</h3>
 <p>Suppose that when someone downloads the app, the app requires them to
 choose a username, which must be different from all other registered
 usernames.</p>
@@ -1419,13 +1319,13 @@ <h3 id="problem-13.1">Problem 13.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
+<h2 class="accordion-header" id="heading12_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_1" aria-expanded="true" aria-controls="collapse12_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_1" class="accordion-collapse collapse"
-aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
+<div id="collapse12_1" class="accordion-collapse collapse"
+aria-labelledby="heading12_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1446,24 +1346,24 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-13.2">Problem 13.2</h3>
+<h3 id="problem-12.2">Problem 12.2</h3>
 <p>What does the code below evaluate to?</p>
-<div class="sourceCode" id="cb17"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>(app_data.take(np.arange(<span class="dv">4</span>))</span>
-<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>         .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_time&#39;</span>)</span>
-<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>         .get(<span class="st">&#39;assembly_time&#39;</span>)</span>
-<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>         .iloc[<span class="dv">0</span>])</span></code></pre></div>
+<div class="sourceCode" id="cb15"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>(app_data.take(np.arange(<span class="dv">4</span>))</span>
+<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>         .sort_values(by<span class="op">=</span><span class="st">&#39;assembly_time&#39;</span>)</span>
+<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>         .get(<span class="st">&#39;assembly_time&#39;</span>)</span>
+<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a>         .iloc[<span class="dv">0</span>])</span></code></pre></div>
 <p><em>Hint:</em> The <code>'assembly_time'</code> column contains
 strings.</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_2" aria-expanded="true" aria-controls="collapse13_2">
+<h2 class="accordion-header" id="heading12_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_2" aria-expanded="true" aria-controls="collapse12_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_2" class="accordion-collapse collapse"
-aria-labelledby="heading13_2" data-bs-parent="#accordionExample">
+<div id="collapse12_2" class="accordion-collapse collapse"
+aria-labelledby="heading12_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1495,7 +1395,7 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-13.3">Problem 13.3</h3>
+<h3 id="problem-12.3">Problem 12.3</h3>
 <p>Complete the implementation of the <code>to_minutes</code> function
 below. This function takes as input a string formatted as
 <code>'x hr, y min'</code> where <code>x</code> and <code>y</code>
@@ -1503,21 +1403,21 @@ <h3 id="problem-13.3">Problem 13.3</h3>
 <strong>as an integer</strong> (type <code>int</code> in Python).</p>
 <p>For example, <code>to_minutes('3 hr, 5 min')</code> should return
 185.</p>
-<div class="sourceCode" id="cb18"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> to_minutes(time):</span>
-<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>    first_split <span class="op">=</span> time.split(<span class="st">&#39; hr, &#39;</span>)</span>
-<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>    second_split <span class="op">=</span> first_split[<span class="dv">1</span>].split(<span class="st">&#39; min&#39;</span>)</span>
-<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
+<div class="sourceCode" id="cb16"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> to_minutes(time):</span>
+<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>    first_split <span class="op">=</span> time.split(<span class="st">&#39; hr, &#39;</span>)</span>
+<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a>    second_split <span class="op">=</span> first_split[<span class="dv">1</span>].split(<span class="st">&#39; min&#39;</span>)</span>
+<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
 <p>What goes in the blank?</p>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_3" aria-expanded="true" aria-controls="collapse13_3">
+<h2 class="accordion-header" id="heading12_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_3" aria-expanded="true" aria-controls="collapse12_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_3" class="accordion-collapse collapse"
-aria-labelledby="heading13_3" data-bs-parent="#accordionExample">
+<div id="collapse12_3" class="accordion-collapse collapse"
+aria-labelledby="heading12_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1581,13 +1481,13 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-13.4">Problem 13.4</h3>
+<h3 id="problem-12.4">Problem 12.4</h3>
 <p>You want to add to <code>app_data</code> a column called
 <code>'minutes'</code> with integer values representing the number of
 minutes it took to assemble each product.</p>
-<div class="sourceCode" id="cb19"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>app_data <span class="op">=</span> app_data.assign(minutes <span class="op">=</span> _________)</span>
-<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>app_data</span></code></pre></div>
+<div class="sourceCode" id="cb17"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>app_data <span class="op">=</span> app_data.assign(minutes <span class="op">=</span> _________)</span>
+<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>app_data</span></code></pre></div>
 <p>Which of the following should go in the blank?</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> <code>to_minutes('assembly_time')</code></p></li>
@@ -1597,13 +1497,13 @@ <h3 id="problem-13.4">Problem 13.4</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading13_4">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_4" aria-expanded="true" aria-controls="collapse13_4">
+<h2 class="accordion-header" id="heading12_4">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse12_4" aria-expanded="true" aria-controls="collapse12_4">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse13_4" class="accordion-collapse collapse"
-aria-labelledby="heading13_4" data-bs-parent="#accordionExample">
+<div id="collapse12_4" class="accordion-collapse collapse"
+aria-labelledby="heading12_4" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -1630,6 +1530,106 @@ <h5>Difficulty: ⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-13">Problem 13</h2>
+<p>In the <code>ikea</code> DataFrame, the first word of each string in
+the <code>'product'</code> column represents the product line. For
+example the HEMNES line of products includes several different products,
+such as beds, dressers, and bedside tables.</p>
+<p>The code below assigns a new column to the <code>ikea</code>
+DataFrame containing the product line associated with each product.</p>
+<div class="sourceCode" id="cb18"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>(ikea.assign(product_line <span class="op">=</span> ikea.get(<span class="st">&#39;product&#39;</span>)</span>
+<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>                                .<span class="bu">apply</span>(extract_product_line)))</span></code></pre></div>
+<p><br></p>
+<h3 id="problem-13.1">Problem 13.1</h3>
+<p>What are the input and output types of the
+<code>extract_product_line</code> function?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> takes a string as input, returns a string</p></li>
+<li><p><input type="radio" disabled="" /> takes a string as input, returns a Series</p></li>
+<li><p><input type="radio" disabled="" /> takes a Series as input, returns a string</p></li>
+<li><p><input type="radio" disabled="" /> takes a Series as input, returns a Series</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading13_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_1" aria-expanded="true" aria-controls="collapse13_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse13_1" class="accordion-collapse collapse"
+aria-labelledby="heading13_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> takes a string as input, returns a
+string</p>
+<p>To use the Series method <code>.apply</code>, we first need a Series,
+containing values of any type. We pass in the name of a function to
+<code>.apply</code> and essentially, <code>.apply</code> calls the given
+function on each value of the Series, producing a Series with the
+resulting outputs of those function calls. In this case,
+<code>.apply(extract_product_line)</code> is called on the Series
+<code>ikea.get('product')</code>, which contains string values. This
+means the function <code>extract_product_line</code> must take strings
+as inputs. We’re told that the code assigns a new column to the
+<code>ikea</code> DataFrame containing the product line associated with
+each product, and we know that the product line is a string, as it’s the
+first word of the product name. This means the function
+<code>extract_product_line</code> must output a string.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 72%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-13.2">Problem 13.2</h3>
+<p>Complete the return statement in the
+<code>extract_product_line</code> function below.</p>
+<div class="sourceCode" id="cb19"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> extract_product_line(x):</span>
+<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> _________</span></code></pre></div>
+<p>What goes in the blank?</p>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading13_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse13_2" aria-expanded="true" aria-controls="collapse13_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse13_2" class="accordion-collapse collapse"
+aria-labelledby="heading13_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> <code>x.split(' ')[0]</code></p>
+<p>This function should take as input a string <code>x</code>,
+representing a product name, and return the first word of that string,
+representing the product line. Since words are separated by spaces, we
+want to split the string on the space character <code>' '</code>.</p>
+<p>It’s also correct to answer <code>x.split()[0]</code> without
+specifying to split on spaces, because the default behavior of the
+string <code>.split</code> method is to split on any whitespace, which
+includes any number of spaces, tabs, newlines, etc. Since we’re only
+extracting the first word, which will be separated from the rest of the
+product name by a single space, it’s equivalent to split using single
+spaces and using the default of any whitespace. </p>
+<hr/>
+<h5>Difficulty:
+⭐️⭐️</h5>
+<p>The average score on this problem was 84%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
 <p class="meta"><em>Source:</em> sp23-midterm — Q2</p>
 <h2 id="problem-14">Problem 14</h2>
 <p>Fill in the blanks below so that the expression evaluates to the most
@@ -1895,7 +1895,7 @@ <h3 id="problem-15.1">Problem 15.1</h3>
 <span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="st">&quot;One&quot;</span> <span class="kw">in</span> s:</span>
 <span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">1</span></span>
 <span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">elif</span> <span class="st">&quot;Two&quot;</span> <span class="kw">in</span> s:</span>
-<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">3</span></span>
+<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">2</span></span>
 <span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a>    <span class="cf">else</span>:</span>
 <span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">3</span></span>
 <span id="cb22-8"><a href="#cb22-8" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="st">&quot;and a half&quot;</span> <span class="kw">in</span> s:</span>
diff --git a/docs/lectures/lec9/index.html b/docs/lectures/lec9/index.html
index c3330d5..fbe6e5d 100644
--- a/docs/lectures/lec9/index.html
+++ b/docs/lectures/lec9/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\..\assets\theme.css" />
+  <link rel="stylesheet" href="../../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
@@ -1121,20 +1121,8 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-12">Problem 12</h2>
-<p>For each offer currently available, the DataFrame <code>offers</code>
-has a separate row for each category of products to which the offer can
-be applied. The columns are:</p>
-<ul>
-<li><code>'offer'</code> (<code>str</code>): the name of the offer</li>
-<li><code>'category'</code> (<code>str</code>): the category to which
-the offer applies</li>
-<li><code>'percent_off'</code> (<code>int</code>): the percent discount
-when applying this offer to this category</li>
-</ul>
-<p>The full <code>offers</code> DataFrame is shown below. All rows are
-pictured.</p>
-<center><img src='../../assets/images/sp22-final/offersdf.png' height=270></center>
-<p><br></p>
+<p>Recall that we have the complete set of currently available discounts
+in the DataFrame <code>offers</code>.</p>
 <p>The DataFrame <code>with_offers</code> is created as follows.</p>
 <div class="sourceCode" id="cb14"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>    (with_offers <span class="op">=</span> ikea.take(np.arange(<span class="dv">6</span>))</span>
@@ -1364,8 +1352,20 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-13">Problem 13</h2>
-<p>Recall that we have the complete set of currently available discounts
-in the DataFrame <code>offers</code>.</p>
+<p>For each offer currently available, the DataFrame <code>offers</code>
+has a separate row for each category of products to which the offer can
+be applied. The columns are:</p>
+<ul>
+<li><code>'offer'</code> (<code>str</code>): the name of the offer</li>
+<li><code>'category'</code> (<code>str</code>): the category to which
+the offer applies</li>
+<li><code>'percent_off'</code> (<code>int</code>): the percent discount
+when applying this offer to this category</li>
+</ul>
+<p>The full <code>offers</code> DataFrame is shown below. All rows are
+pictured.</p>
+<center><img src='../../assets/images/sp22-final/offersdf.png' height=270></center>
+<p><br></p>
 <p>The DataFrame <code>with_offers</code> is created as follows.</p>
 <div class="sourceCode" id="cb17"><pre
 class="sourceCode py"><code class="sourceCode python"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>    (with_offers <span class="op">=</span> ikea.take(np.arange(<span class="dv">6</span>))</span>
@@ -4233,51 +4233,11 @@ <h5>Difficulty: ⭐️⭐️⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-29">Problem 29</h2>
-<p>If we merge a table with <code>n</code> rows with a table with
-<code>m</code> rows, how many rows does the resulting table have?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> <code>n</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>m</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>max(m,n)</code></p></li>
-<li><p><input type="radio" disabled="" /> <code>m * n</code></p></li>
-<li><p><input type="radio" disabled="" /> not enough information to tell</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading29">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29" aria-expanded="true" aria-controls="collapse29">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse29" class="accordion-collapse collapse"
-aria-labelledby="heading29" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> not enough information to tell</p>
-<p>The question does not provide enough information to know the
-resulting table size with certainty. When merging two tables together,
-the tables can be merged with a inner, left, right, and outer join. Each
-of these joins will produce a different amount of rows. Since the
-question does not provide the type of join, it is impossible to tell the
-resulting table size.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 74%.</p>
-</div>
-</div>
-</div>
-</div>
-<hr />
-<h2 id="problem-30">Problem 30</h2>
 <p>You are given a table called books that contains columns
 <code>'author'</code> (<code>str</code>), <code>'title'</code>
 (<code>str</code>), <code>'num_chapters'</code> (<code>int</code>), and
 <code>'publication_year'</code> (<code>int</code>). <br></p>
-<h3 id="problem-30.1">Problem 30.1</h3>
+<h3 id="problem-29.1">Problem 29.1</h3>
 <p>What will be the output of the following code?
 <code>books.groupby(“publication_year”).mean().shape[1]</code></p>
 <ul class="task-list">
@@ -4288,13 +4248,13 @@ <h3 id="problem-30.1">Problem 30.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading30_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_1" aria-expanded="true" aria-controls="collapse30_1">
+<h2 class="accordion-header" id="heading29_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse29_1" aria-expanded="true" aria-controls="collapse29_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse30_1" class="accordion-collapse collapse"
-aria-labelledby="heading30_1" data-bs-parent="#accordionExample">
+<div id="collapse29_1" class="accordion-collapse collapse"
+aria-labelledby="heading29_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4320,12 +4280,12 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-31">Problem 31</h2>
+<h2 id="problem-30">Problem 30</h2>
 <p>You are given a table called books that contains columns
 <code>'author'</code> (<code>str</code>), <code>'title'</code>
 (<code>str</code>), <code>'num_chapters'</code> (<code>int</code>), and
 <code>'publication_year'</code> (<code>int</code>). <br></p>
-<h3 id="problem-31.1">Problem 31.1</h3>
+<h3 id="problem-30.1">Problem 30.1</h3>
 <p>What will be the output of the following code?
 <code>books.groupby(“publication_year”).mean().shape[1]</code></p>
 <ul class="task-list">
@@ -4336,13 +4296,13 @@ <h3 id="problem-31.1">Problem 31.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_1" aria-expanded="true" aria-controls="collapse31_1">
+<h2 class="accordion-header" id="heading30_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_1" aria-expanded="true" aria-controls="collapse30_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_1" class="accordion-collapse collapse"
-aria-labelledby="heading31_1" data-bs-parent="#accordionExample">
+<div id="collapse30_1" class="accordion-collapse collapse"
+aria-labelledby="heading30_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4367,7 +4327,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.2">Problem 31.2</h3>
+<h3 id="problem-30.2">Problem 30.2</h3>
 <p>Which of the following strategies would work to compute the absolute
 difference in the average number of chapters per book for authors “Dean
 Koontz” and “Charles Dickens”?</p>
@@ -4395,13 +4355,13 @@ <h3 id="problem-31.2">Problem 31.2</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_2" aria-expanded="true" aria-controls="collapse31_2">
+<h2 class="accordion-header" id="heading30_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_2" aria-expanded="true" aria-controls="collapse30_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_2" class="accordion-collapse collapse"
-aria-labelledby="heading31_2" data-bs-parent="#accordionExample">
+<div id="collapse30_2" class="accordion-collapse collapse"
+aria-labelledby="heading30_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4430,7 +4390,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-31.3">Problem 31.3</h3>
+<h3 id="problem-30.3">Problem 30.3</h3>
 <p>Which of the following will produce the same value as the total
 number of books in the table?</p>
 <ul class="task-list">
@@ -4440,13 +4400,13 @@ <h3 id="problem-31.3">Problem 31.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading31_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31_3" aria-expanded="true" aria-controls="collapse31_3">
+<h2 class="accordion-header" id="heading30_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse30_3" aria-expanded="true" aria-controls="collapse30_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse31_3" class="accordion-collapse collapse"
-aria-labelledby="heading31_3" data-bs-parent="#accordionExample">
+<div id="collapse30_3" class="accordion-collapse collapse"
+aria-labelledby="heading30_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4470,6 +4430,46 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
+<h2 id="problem-31">Problem 31</h2>
+<p>If we merge a table with <code>n</code> rows with a table with
+<code>m</code> rows, how many rows does the resulting table have?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> <code>n</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>m</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>max(m,n)</code></p></li>
+<li><p><input type="radio" disabled="" /> <code>m * n</code></p></li>
+<li><p><input type="radio" disabled="" /> not enough information to tell</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading31">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse31" aria-expanded="true" aria-controls="collapse31">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse31" class="accordion-collapse collapse"
+aria-labelledby="heading31" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer: </strong> not enough information to tell</p>
+<p>The question does not provide enough information to know the
+resulting table size with certainty. When merging two tables together,
+the tables can be merged with a inner, left, right, and outer join. Each
+of these joins will produce a different amount of rows. Since the
+question does not provide the type of join, it is impossible to tell the
+resulting table size.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 74%.</p>
+</div>
+</div>
+</div>
+</div>
+<hr />
 <h2 id="problem-32">Problem 32</h2>
 <p>Give an example of a dataset and a question you would want to answer
 about that dataset which you would answer by grouping with subgroups
@@ -4540,154 +4540,11 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <h2 id="problem-33">Problem 33</h2>
 <p><br></p>
 <h3 id="problem-33.1">Problem 33.1</h3>
-<p>What type of visualization is best suited for visualizing the trend
-in the number of points Kelsey Plum scored per game in 2021?</p>
-<ul class="task-list">
-<li><p><input type="radio" disabled="" /> Histogram</p></li>
-<li><p><input type="radio" disabled="" /> Bar chart</p></li>
-<li><p><input type="radio" disabled="" /> Line chart</p></li>
-<li><p><input type="radio" disabled="" /> Scatter plot</p></li>
-</ul>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading33_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_1" aria-expanded="true" aria-controls="collapse33_1">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse33_1" class="accordion-collapse collapse"
-aria-labelledby="heading33_1" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer: </strong> Line chart</p>
-<p>Here, there are two quantitative variables (number of points and game
-number), and one of them involves some element of time (game number).
-Line charts are appropriate when one quantitative variable is time.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 75%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-33.2">Problem 33.2</h3>
-<p>Fill in the blanks below so that <code>total_june</code> evaluates to
-the total number of points Kelsey Plum scored in June.</p>
-<div class="sourceCode" id="cb52"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a>june_only <span class="op">=</span> plum[__(a)__]</span>
-<span id="cb52-2"><a href="#cb52-2" aria-hidden="true" tabindex="-1"></a>total_june <span class="op">=</span> june_only.__(b)__</span></code></pre></div>
-<ol type="1">
-<li><p>What goes in blank (a)?</p></li>
-<li><p>What goes in blank (b)?</p></li>
-</ol>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading33_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_2" aria-expanded="true" aria-controls="collapse33_2">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse33_2" class="accordion-collapse collapse"
-aria-labelledby="heading33_2" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong></p>
-<ol type="1">
-<li><p><code>plum.get('Date').str.contains('-06-')</code></p></li>
-<li><p><code>get('PTS').sum()</code></p></li>
-</ol>
-<p>To find the total number of points Kelsey Plum scored in June, one
-approach is to first create a DataFrame with only the rows for June.
-During the month of June, the <code>'Date'</code> values contain
-<code>'-06-'</code> (since June is the 6th month), so
-<code>plum.get('Date').str.contains('-06-')</code> is a Series
-containing <code>True</code> only for the June rows and
-<code>june_only = plum[plum.get('Date').str.contains('-06-')]</code> is
-a DataFrame containing only the June rows.</p>
-<p>Then, all we need is the sum of the <code>'PTS'</code> column, which
-is given by <code>june_only.get('PTS').sum()</code>.</p>
-<hr/>
-<h5>Difficulty: ⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 90%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<h3 id="problem-33.3">Problem 33.3</h3>
-<p>For your convenience, we show the first few rows of <code>plum</code>
-again below.</p>
-<center><img src='../../assets/images/wi22-final/plum.png' width=40%></center>
-<p>There is exactly one team in the WNBA that Plum’s team did not win
-any games against during the 2021 season. Fill in the blanks below so
-that <code>never_beat</code> evaluates to a string containing the
-three-letter code of that team.</p>
-<div class="sourceCode" id="cb53"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>never_beat <span class="op">=</span> plum.groupby(__(a)__).<span class="bu">sum</span>().__(b)__</span></code></pre></div>
-<ol type="1">
-<li><p>What goes in blank (a)?</p></li>
-<li><p>What goes in blank (b)?</p></li>
-</ol>
-<div id="accordionExample" class="accordion">
-<div class="accordion-item">
-<h2 class="accordion-header" id="heading33_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_3" aria-expanded="true" aria-controls="collapse33_3">
-Click to view the solution.
-</button>
-</h2>
-<div id="collapse33_3" class="accordion-collapse collapse"
-aria-labelledby="heading33_3" data-bs-parent="#accordionExample">
-<div class="accordion-body">
-<header id="title-block-header">
-<h1 class="title"> </h1>
-</header>
-<p><strong>Answer:</strong></p>
-<ol type="1">
-<li><p><code>'Opp'</code></p></li>
-<li><p><code>sort_values('Won').index[0]</code></p></li>
-</ol>
-<p>The key insight here is that the values in the <code>'Won'</code>
-column are Boolean, and when Boolean values are used in arithmetic they
-are treated as 1s (<code>True</code>) and 0s (<code>False</code>). The
-<code>sum</code> of several <code>'Won'</code> values is the same as the
-number of wins.</p>
-<p>If we group <code>plum</code> by <code>'Opp'</code> and use
-<code>.sum()</code>, the resulting <code>'Won'</code> column contains
-the number of wins that Plum’s team had against each unique opponent. If
-we sort this DataFrame by <code>'Won'</code> in increasing order (which
-is the default behavior of <code>sort_values</code>), the row at the top
-will correspond to the <code>'Opp'</code> that Plum’s team had no wins
-against. Since we grouped by <code>'Opp'</code>, team names are stored
-in the index, so <code>.index[0]</code> will give us the name of the
-desired team.</p>
-<hr/>
-<h5>Difficulty: ⭐️⭐️⭐️</h5>
-<p>
-</p>
-<p>The average score on this problem was 67%.</p>
-</div>
-</div>
-</div>
-</div>
-<p><br></p>
-<hr />
-<h2 id="problem-34">Problem 34</h2>
-<p><br></p>
-<h3 id="problem-34.1">Problem 34.1</h3>
 <p>Consider the function <code>unknown</code>, defined below.</p>
-<div class="sourceCode" id="cb54"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> unknown(df):</span>
-<span id="cb54-2"><a href="#cb54-2" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> plum.groupby(<span class="st">&#39;Opp&#39;</span>).<span class="bu">max</span>().get([<span class="st">&#39;Date&#39;</span>, <span class="st">&#39;PTS&#39;</span>])</span>
-<span id="cb54-3"><a href="#cb54-3" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> np.array(grouped.reset_index().index)[df]</span></code></pre></div>
+<div class="sourceCode" id="cb52"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> unknown(df):</span>
+<span id="cb52-2"><a href="#cb52-2" aria-hidden="true" tabindex="-1"></a>    grouped <span class="op">=</span> plum.groupby(<span class="st">&#39;Opp&#39;</span>).<span class="bu">max</span>().get([<span class="st">&#39;Date&#39;</span>, <span class="st">&#39;PTS&#39;</span>])</span>
+<span id="cb52-3"><a href="#cb52-3" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> np.array(grouped.reset_index().index)[df]</span></code></pre></div>
 <p>What does <code>unknown(3)</code> evaluate to?</p>
 <ul class="task-list">
 <li><p><input type="radio" disabled="" /> <code>'2021-06-05'</code></p></li>
@@ -4701,13 +4558,13 @@ <h3 id="problem-34.1">Problem 34.1</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading34_1">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse34_1" aria-expanded="true" aria-controls="collapse34_1">
+<h2 class="accordion-header" id="heading33_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_1" aria-expanded="true" aria-controls="collapse33_1">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse34_1" class="accordion-collapse collapse"
-aria-labelledby="heading34_1" data-bs-parent="#accordionExample">
+<div id="collapse33_1" class="accordion-collapse collapse"
+aria-labelledby="heading33_1" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4748,7 +4605,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-34.2">Problem 34.2</h3>
+<h3 id="problem-33.2">Problem 33.2</h3>
 <p>For your convenience, we show the first few rows of <code>plum</code>
 again below.</p>
 <center><img src='../../assets/images/wi22-final/plum.png' width=40%></center>
@@ -4757,21 +4614,21 @@ <h3 id="problem-34.2">Problem 34.2</h3>
 won at least one game in an opponent’s arena and lost at least one game
 in an opponent’s arena.</p>
 <p>Consider the DataFrame <code>home_won</code>, defined below.</p>
-<div class="sourceCode" id="cb55"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>home_won <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).mean().reset_index()</span></code></pre></div>
+<div class="sourceCode" id="cb53"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>home_won <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).mean().reset_index()</span></code></pre></div>
 <ol type="1">
 <li><p>How many rows does <code>home_won</code> have?</p></li>
 <li><p>How many columns does <code>home_won</code> have?</p></li>
 </ol>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading34_2">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse34_2" aria-expanded="true" aria-controls="collapse34_2">
+<h2 class="accordion-header" id="heading33_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_2" aria-expanded="true" aria-controls="collapse33_2">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse34_2" class="accordion-collapse collapse"
-aria-labelledby="heading34_2" data-bs-parent="#accordionExample">
+<div id="collapse33_2" class="accordion-collapse collapse"
+aria-labelledby="heading33_2" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4816,16 +4673,16 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 </div>
 <p><br></p>
-<h3 id="problem-34.3">Problem 34.3</h3>
+<h3 id="problem-33.3">Problem 33.3</h3>
 <p>Consider the DataFrame <code>home_won</code> once again.</p>
-<div class="sourceCode" id="cb56"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>home_won <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).mean().reset_index()</span></code></pre></div>
+<div class="sourceCode" id="cb54"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>home_won <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).mean().reset_index()</span></code></pre></div>
 <p>Now consider the DataFrame <code>puzzle</code>, defined below. Note
 that the only difference between <code>home_won</code> and
 <code>puzzle</code> is the use of <code>.count()</code> instead of
 <code>.mean()</code>.</p>
-<div class="sourceCode" id="cb57"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>puzzle <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).count().reset_index()</span></code></pre></div>
+<div class="sourceCode" id="cb55"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>puzzle <span class="op">=</span> plum.groupby([<span class="st">&#39;Home&#39;</span>, <span class="st">&#39;Won&#39;</span>]).count().reset_index()</span></code></pre></div>
 <p>How do the number of rows and columns in <code>home_won</code>
 compare to the number of rows and columns in <code>puzzle</code>?</p>
 <ul class="task-list">
@@ -4840,13 +4697,13 @@ <h3 id="problem-34.3">Problem 34.3</h3>
 </ul>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
-<h2 class="accordion-header" id="heading34_3">
-<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse34_3" aria-expanded="true" aria-controls="collapse34_3">
+<h2 class="accordion-header" id="heading33_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse33_3" aria-expanded="true" aria-controls="collapse33_3">
 Click to view the solution.
 </button>
 </h2>
-<div id="collapse34_3" class="accordion-collapse collapse"
-aria-labelledby="heading34_3" data-bs-parent="#accordionExample">
+<div id="collapse33_3" class="accordion-collapse collapse"
+aria-labelledby="heading33_3" data-bs-parent="#accordionExample">
 <div class="accordion-body">
 <header id="title-block-header">
 <h1 class="title"> </h1>
@@ -4878,21 +4735,75 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <p><br></p>
 <hr />
-<h2 id="problem-35">Problem 35</h2>
+<h2 id="problem-34">Problem 34</h2>
 <p><br></p>
-<h3 id="problem-35.1">Problem 35.1</h3>
+<h3 id="problem-34.1">Problem 34.1</h3>
 <p>There is exactly one team in the WNBA that Plum’s team did not win
 any games against during the 2021 season. Fill in the blanks below so
 that <code>never_beat</code> evaluates to a string containing the
 three-letter code of that team.</p>
-<div class="sourceCode" id="cb58"><pre
-class="sourceCode py"><code class="sourceCode python"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>never_beat <span class="op">=</span> plum.groupby(__(a)__).<span class="bu">sum</span>().__(b)__</span></code></pre></div>
+<div class="sourceCode" id="cb56"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>never_beat <span class="op">=</span> plum.groupby(__(a)__).<span class="bu">sum</span>().__(b)__</span></code></pre></div>
 <ol type="1">
 <li><p>What goes in blank (a)?</p></li>
 <li><p>What goes in blank (b)?</p></li>
 </ol>
 <div id="accordionExample" class="accordion">
 <div class="accordion-item">
+<h2 class="accordion-header" id="heading34_1">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse34_1" aria-expanded="true" aria-controls="collapse34_1">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse34_1" class="accordion-collapse collapse"
+aria-labelledby="heading34_1" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong></p>
+<ol type="1">
+<li><p><code>'Opp'</code></p></li>
+<li><p><code>sort_values('Won').index[0]</code></p></li>
+</ol>
+<p>The key insight here is that the values in the <code>'Won'</code>
+column are Boolean, and when Boolean values are used in arithmetic they
+are treated as 1s (<code>True</code>) and 0s (<code>False</code>). The
+<code>sum</code> of several <code>'Won'</code> values is the same as the
+number of wins.</p>
+<p>If we group <code>plum</code> by <code>'Opp'</code> and use
+<code>.sum()</code>, the resulting <code>'Won'</code> column contains
+the number of wins that Plum’s team had against each unique opponent. If
+we sort this DataFrame by <code>'Won'</code> in increasing order (which
+is the default behavior of <code>sort_values</code>), the row at the top
+will correspond to the <code>'Opp'</code> that Plum’s team had no wins
+against. Since we grouped by <code>'Opp'</code>, team names are stored
+in the index, so <code>.index[0]</code> will give us the name of the
+desired team.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 67%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<hr />
+<h2 id="problem-35">Problem 35</h2>
+<p><br></p>
+<h3 id="problem-35.1">Problem 35.1</h3>
+<p>What type of visualization is best suited for visualizing the trend
+in the number of points Kelsey Plum scored per game in 2021?</p>
+<ul class="task-list">
+<li><p><input type="radio" disabled="" /> Histogram</p></li>
+<li><p><input type="radio" disabled="" /> Bar chart</p></li>
+<li><p><input type="radio" disabled="" /> Line chart</p></li>
+<li><p><input type="radio" disabled="" /> Scatter plot</p></li>
+</ul>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
 <h2 class="accordion-header" id="heading35_1">
 <button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse35_1" aria-expanded="true" aria-controls="collapse35_1">
 Click to view the solution.
@@ -4904,6 +4815,95 @@ <h2 class="accordion-header" id="heading35_1">
 <header id="title-block-header">
 <h1 class="title"> </h1>
 </header>
+<p><strong>Answer: </strong> Line chart</p>
+<p>Here, there are two quantitative variables (number of points and game
+number), and one of them involves some element of time (game number).
+Line charts are appropriate when one quantitative variable is time.</p>
+<hr/>
+<h5>Difficulty: ⭐️⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 75%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-35.2">Problem 35.2</h3>
+<p>Fill in the blanks below so that <code>total_june</code> evaluates to
+the total number of points Kelsey Plum scored in June.</p>
+<div class="sourceCode" id="cb57"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>june_only <span class="op">=</span> plum[__(a)__]</span>
+<span id="cb57-2"><a href="#cb57-2" aria-hidden="true" tabindex="-1"></a>total_june <span class="op">=</span> june_only.__(b)__</span></code></pre></div>
+<ol type="1">
+<li><p>What goes in blank (a)?</p></li>
+<li><p>What goes in blank (b)?</p></li>
+</ol>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading35_2">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse35_2" aria-expanded="true" aria-controls="collapse35_2">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse35_2" class="accordion-collapse collapse"
+aria-labelledby="heading35_2" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
+<p><strong>Answer:</strong></p>
+<ol type="1">
+<li><p><code>plum.get('Date').str.contains('-06-')</code></p></li>
+<li><p><code>get('PTS').sum()</code></p></li>
+</ol>
+<p>To find the total number of points Kelsey Plum scored in June, one
+approach is to first create a DataFrame with only the rows for June.
+During the month of June, the <code>'Date'</code> values contain
+<code>'-06-'</code> (since June is the 6th month), so
+<code>plum.get('Date').str.contains('-06-')</code> is a Series
+containing <code>True</code> only for the June rows and
+<code>june_only = plum[plum.get('Date').str.contains('-06-')]</code> is
+a DataFrame containing only the June rows.</p>
+<p>Then, all we need is the sum of the <code>'PTS'</code> column, which
+is given by <code>june_only.get('PTS').sum()</code>.</p>
+<hr/>
+<h5>Difficulty: ⭐️</h5>
+<p>
+</p>
+<p>The average score on this problem was 90%.</p>
+</div>
+</div>
+</div>
+</div>
+<p><br></p>
+<h3 id="problem-35.3">Problem 35.3</h3>
+<p>For your convenience, we show the first few rows of <code>plum</code>
+again below.</p>
+<center><img src='../../assets/images/wi22-final/plum.png' width=40%></center>
+<p>There is exactly one team in the WNBA that Plum’s team did not win
+any games against during the 2021 season. Fill in the blanks below so
+that <code>never_beat</code> evaluates to a string containing the
+three-letter code of that team.</p>
+<div class="sourceCode" id="cb58"><pre
+class="sourceCode py"><code class="sourceCode python"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>never_beat <span class="op">=</span> plum.groupby(__(a)__).<span class="bu">sum</span>().__(b)__</span></code></pre></div>
+<ol type="1">
+<li><p>What goes in blank (a)?</p></li>
+<li><p>What goes in blank (b)?</p></li>
+</ol>
+<div id="accordionExample" class="accordion">
+<div class="accordion-item">
+<h2 class="accordion-header" id="heading35_3">
+<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#collapse35_3" aria-expanded="true" aria-controls="collapse35_3">
+Click to view the solution.
+</button>
+</h2>
+<div id="collapse35_3" class="accordion-collapse collapse"
+aria-labelledby="heading35_3" data-bs-parent="#accordionExample">
+<div class="accordion-body">
+<header id="title-block-header">
+<h1 class="title"> </h1>
+</header>
 <p><strong>Answer:</strong></p>
 <ol type="1">
 <li><p><code>'Opp'</code></p></li>
diff --git a/docs/sp24-final/index.html b/docs/sp24-final/index.html
index 4b2212c..3cacc79 100644
--- a/docs/sp24-final/index.html
+++ b/docs/sp24-final/index.html
@@ -2396,7 +2396,7 @@ <h3 id="problem-13.1">Problem 13.1</h3>
 <span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="st">&quot;One&quot;</span> <span class="kw">in</span> s:</span>
 <span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">1</span></span>
 <span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>    <span class="cf">elif</span> <span class="st">&quot;Two&quot;</span> <span class="kw">in</span> s:</span>
-<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">3</span></span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">2</span></span>
 <span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>    <span class="cf">else</span>:</span>
 <span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>        n_baths <span class="op">=</span> <span class="dv">3</span></span>
 <span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>    <span class="cf">if</span> <span class="st">&quot;and a half&quot;</span> <span class="kw">in</span> s:</span>
diff --git a/docs/sp25-final/index.html b/docs/sp25-final/index.html
index 281e04a..b355ea6 100644
--- a/docs/sp25-final/index.html
+++ b/docs/sp25-final/index.html
@@ -6,6 +6,9 @@
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
   <title>Spring 2025 Final Exam</title>
   <style>
+    /* Default styles provided by pandoc.
+    ** See https://pandoc.org/MANUAL.html#variables-for-html for config info.
+    */
     code{white-space: pre-wrap;}
     span.smallcaps{font-variant: small-caps;}
     div.columns{display: flex; gap: min(4vw, 1.5em);}
@@ -21,8 +24,9 @@
       vertical-align: middle;
     }
     /* CSS for syntax highlighting */
+    html { -webkit-text-size-adjust: 100%; }
     pre > code.sourceCode { white-space: pre; position: relative; }
-    pre > code.sourceCode > span { line-height: 1.25; }
+    pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
     pre > code.sourceCode > span:empty { height: 1.2em; }
     .sourceCode { overflow: visible; }
     code.sourceCode > span { color: inherit; text-decoration: inherit; }
@@ -33,7 +37,7 @@
     }
     @media print {
     pre > code.sourceCode { white-space: pre-wrap; }
-    pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
+    pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
     }
     pre.numberSource code
       { counter-reset: source-line 0; }
@@ -87,7 +91,7 @@
   </style>
   <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
-  src="https://cdn.jsdelivr.net/npm/katex@0.15.1/dist/katex.min.js"></script>
+  src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
  var mathElements = document.getElementsByClassName("math");
  var macros = [];
@@ -103,7 +107,7 @@
 }}});
   </script>
   <link rel="stylesheet"
-  href="https://cdn.jsdelivr.net/npm/katex@0.15.1/dist/katex.min.css" />
+  href="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.css" />
 </head>
 <body>
 <header id="title-block-header">
@@ -162,7 +166,7 @@ <h1 class="title">Spring 2025 Final Exam</h1>
 </ul>
 <hr />
 <h2 id="problem-1">Problem 1</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 15</span></div></p>
 <p>In an annual ceremony known as the reaping, tributes are selected to
@@ -317,7 +321,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-2">Problem 2</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 11</span></div></p>
 <p>As we saw in the last problem, children aged <span
@@ -460,7 +464,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-3">Problem 3</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 4</span></div></p>
 <p>So far, we have seen one way that children have tickets entered into
@@ -660,7 +664,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-4">Problem 4</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 10</span></div></p>
 <p>After being selected at the reaping, tributes are transported to the
@@ -766,7 +770,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 </div>
 <hr />
 <h2 id="problem-5">Problem 5</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 15</span></div></p>
 <p>The night before the Hunger Games begins, each tribute is interviewed
@@ -1040,12 +1044,21 @@ <h2 class="accordion-header" id="heading5_5">
 <h1 class="title"> </h1>
 </header>
 <p><strong>Answer</strong>: Our new sample should have four times as
-many people overall. It doesn’t matter how many of them are from
-District 12.</p>
-<p>The width of our confidence interval is determined by the standard
-error which decreases at the factor of <span class="math inline">\frac{1}{\sqrt(n)}</span> to half the width, we need
-the denominator to increase by a factor of 2. Therefore, we need 4x more
-data, as the square root of 4 is 2.</p>
+many people from District 12. It doesn’t matter how many people the
+sample contains overall.</p>
+<p>The width of a confidence interval gets smaller as we collect more
+data, and it shrinks proportional to <span class="math inline">\frac{1}{\sqrt{n}}</span>, where n is the sample
+size.</p>
+<p>If we want the interval to be <strong>half as wide</strong>, we need
+<span class="math inline">\frac{1}{\sqrt{n}}</span> to be cut in half,
+which means n must become <strong>four times as large</strong>:</p>
+<p><span class="math display">
+\frac{1}{\sqrt{n_{\text{new}}}}
+= \frac{1}{\sqrt{4n}}
+= \frac{1}{2\sqrt{n}}
+\;\Longrightarrow\;
+n_{\text{new}} = 4n.
+</span></p>
 <hr/>
 <h5>Difficulty: ⭐️⭐️</h5>
 <p>
@@ -1058,7 +1071,7 @@ <h5>Difficulty: ⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-6">Problem 6</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 21</span></div></p>
 <p>Residents of Panem not participating in the Hunger Games can sponsor
@@ -1075,7 +1088,7 @@ <h2 id="problem-6">Problem 6</h2>
 </p>
 <table>
 <thead>
-<tr class="header">
+<tr>
 <th style="text-align: left;"><strong>Category</strong></th>
 <th style="text-align: left;">Medical</th>
 <th style="text-align: left;">Food</th>
@@ -1086,7 +1099,7 @@ <h2 id="problem-6">Problem 6</h2>
 </tr>
 </thead>
 <tbody>
-<tr class="odd">
+<tr>
 <td style="text-align: left;"><strong>Count</strong></td>
 <td style="text-align: left;"><span class="math inline">40</span></td>
 <td style="text-align: left;"><span class="math inline">30</span></td>
@@ -1107,7 +1120,7 @@ <h2 id="problem-6">Problem 6</h2>
 </p>
 <table>
 <thead>
-<tr class="header">
+<tr>
 <th style="text-align: left;"><strong>Category</strong></th>
 <th style="text-align: left;">Medical</th>
 <th style="text-align: left;">Food</th>
@@ -1118,7 +1131,7 @@ <h2 id="problem-6">Problem 6</h2>
 </tr>
 </thead>
 <tbody>
-<tr class="odd">
+<tr>
 <td style="text-align: left;"><strong>Count</strong></td>
 <td style="text-align: left;"><span class="math inline">700</span></td>
 <td style="text-align: left;"><span class="math inline">500</span></td>
@@ -1191,7 +1204,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </p>
 <table>
 <thead>
-<tr class="header">
+<tr>
 <th style="text-align: left;"><strong>Category</strong></th>
 <th style="text-align: left;">Medical</th>
 <th style="text-align: left;">Food</th>
@@ -1202,7 +1215,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </tr>
 </thead>
 <tbody>
-<tr class="odd">
+<tr>
 <td style="text-align: left;"><strong>Count</strong></td>
 <td style="text-align: left;"><span class="math inline">40</span></td>
 <td style="text-align: left;"><span class="math inline">30</span></td>
@@ -1219,7 +1232,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </p>
 <table>
 <thead>
-<tr class="header">
+<tr>
 <th style="text-align: left;"><strong>Category</strong></th>
 <th style="text-align: left;">Medical</th>
 <th style="text-align: left;">Food</th>
@@ -1230,7 +1243,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 </tr>
 </thead>
 <tbody>
-<tr class="odd">
+<tr>
 <td style="text-align: left;"><strong>Count</strong></td>
 <td style="text-align: left;"><span class="math inline">700</span></td>
 <td style="text-align: left;"><span class="math inline">500</span></td>
@@ -1345,7 +1358,7 @@ <h5>Difficulty: ⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-7">Problem 7</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 25</span></div></p>
 <p>During the Hunger Games, sponsors may purchase supplies for the
@@ -1500,7 +1513,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-8">Problem 8</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 20</span></div></p>
 <p>[(13 pts)]</p>
@@ -1671,7 +1684,7 @@ <h5>Difficulty: ⭐️⭐️⭐️</h5>
 <p><br></p>
 <hr />
 <h2 id="problem-9">Problem 9</h2>
-<div class='meta'>
+<div class="meta">
 <p><span class="pill pill-lecture" title="Lecture number(s)">Lecture
 16</span></div></p>
 <p>Before getting selected for the Hunger Games, Katniss often spent her
@@ -1689,26 +1702,26 @@ <h3 id="problem-9.1">Problem 9.1</h3>
 integers.</p>
 <table>
 <thead>
-<tr class="header">
+<tr>
 <th style="text-align: left;"><strong>Sample</strong></th>
 <th style="text-align: center;"><strong>Mean</strong></th>
 <th style="text-align: center;"><strong>Variance</strong></th>
 </tr>
 </thead>
 <tbody>
-<tr class="odd">
+<tr>
 <td
 style="text-align: left;"><code>a.) katniss_sample = [47, 44, 50]</code></td>
 <td style="text-align: center;"></td>
 <td style="text-align: center;"></td>
 </tr>
-<tr class="even">
+<tr>
 <td
 style="text-align: left;"><code>b.) gale_sample = [25, 28, 28]</code></td>
 <td style="text-align: center;"></td>
 <td style="text-align: center;"></td>
 </tr>
-<tr class="odd">
+<tr>
 <td
 style="text-align: left;"><code>c.) average_sample = [36, 36, 39]</code></td>
 <td style="text-align: center;"></td>
@@ -1855,5 +1868,14 @@ <h2 id="section"><span class="math display"> </span></h2>
 <a href="https://forms.gle/WZ71FchnXU1K154d7">Let us know
 here</u></a>.</h4>
 <hr />
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
+</div>
 </body>
 </html>
diff --git a/docs/sp25-quiz3/index.html b/docs/sp25-quiz3/index.html
index f128dfc..2df4ccd 100644
--- a/docs/sp25-quiz3/index.html
+++ b/docs/sp25-quiz3/index.html
@@ -24,7 +24,7 @@
       vertical-align: middle;
     }
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/docs/sp25-quiz5/index.html b/docs/sp25-quiz5/index.html
index a4feeda..1dac5c8 100644
--- a/docs/sp25-quiz5/index.html
+++ b/docs/sp25-quiz5/index.html
@@ -89,7 +89,7 @@
     code span.vs { color: #4070a0; } /* VerbatimString */
     code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
   </style>
-  <link rel="stylesheet" href="..\assets\theme.css" />
+  <link rel="stylesheet" href="../assets/theme.css" />
   <script defer=""
   src="https://cdn.jsdelivr.net/npm/katex@latest/dist/katex.min.js"></script>
   <script>document.addEventListener("DOMContentLoaded", function () {
diff --git a/problems/sp24-final/q13.md b/problems/sp24-final/q13.md
index 641b243..abe0a98 100644
--- a/problems/sp24-final/q13.md
+++ b/problems/sp24-final/q13.md
@@ -13,7 +13,7 @@ def float_bath(s):
     if "One" in s:
         n_baths = 1
     elif "Two" in s:
-        n_baths = 3
+        n_baths = 2
     else:
         n_baths = 3
     if "and a half" in s:
diff --git a/problems/sp25-final/q05.md b/problems/sp25-final/q05.md
index 88865bf..c4da6b6 100644
--- a/problems/sp25-final/q05.md
+++ b/problems/sp25-final/q05.md
@@ -168,9 +168,21 @@ Which of the following best describes how to achieve this?
 
 # BEGIN SOLUTION
 
-**Answer**: Our new sample should have four times as many people overall. It doesn't matter how many of them are from District 12.
+**Answer**: Our new sample should have four times as many people from District 12. It doesn't matter how many people the sample contains overall.
+
+The width of a confidence interval gets smaller as we collect more data, and it shrinks proportional to $\frac{1}{\sqrt{n}}$, where n is the sample size.
+
+If we want the interval to be **half as wide**, we need $\frac{1}{\sqrt{n}}$ to be cut in half, which means n must become **four times as large**:
+
+$$
+\frac{1}{\sqrt{n_{\text{new}}}}
+= \frac{1}{\sqrt{4n}}
+= \frac{1}{2\sqrt{n}}
+\;\Longrightarrow\;
+n_{\text{new}} = 4n.
+$$
+
 
-The width of our confidence interval is determined by the standard error which decreases at the factor of $\frac{1}{\sqrt(n)}$ to half the width, we need the denominator to increase by a factor of 2. Therefore, we need 4x more data, as the square root of 4 is 2.
 
 <average>75</average>