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e27b12ec » smenks13
2012-03-06 New exercise: Z-scores 2: Reading a z-table
1 <!DOCTYPE html>
c50b7558 » smenks13
2012-03-13 @beneater changes
2 <html data-require="math graphie word-problems stat">
e27b12ec » smenks13
2012-03-06 New exercise: Z-scores 2: Reading a z-table
3 <head>
9fdecffe » beneater
2012-04-16 Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
4 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
5 <title>Z-scores 2: Reading a z-table</title>
6 <script src="../khan-exercise.js"></script>
7 <style>
8 .reading span {
9 width: 32px;
10 font-size: 11px;
11 padding: 5px;
12 }
13 .reading span:first-child {
14 font-weight: bold;
15 width: 22px;
16 border-right: 2px solid #CCCCCC;
17 }
18 </style>
e27b12ec » smenks13
2012-03-06 New exercise: Z-scores 2: Reading a z-table
19 </head>
20 <body>
9fdecffe » beneater
2012-04-16 Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
21 <div class="exercise">
22 <div class="problems">
23 <div>
24 <div class="vars">
25 <var id="COL_INDEX">randRange(0, 9)</var>
26 <var id="ROW_INDEX">randRange(0, 9)</var>
27 <var id="ZSCORE">roundTo(2, randRange(0, 2) + ROW_INDEX / 10 + COL_INDEX / 100)</var>
28 <var id="GRADE">randRange(70, 90)</var>
29 <var id="STDDEV">randRange(2, 6)</var>
30 <var id="MEAN">roundTo(2, GRADE - ZSCORE * STDDEV)</var>
31 <var id="ROWS">
32 (function() {
33 var rowNames = [];
34 for(var i = floorTo(0, ZSCORE); i &lt; (floorTo(0, ZSCORE) + 1); i += 0.1) {
35 rowNames.push(i.toFixed(1));
36 }
37 return rowNames;
38 })()
39 </var>
40 <var id="COLUMNS">[".00", ".01", ".02", ".03", ".04", ".05", ".06", ".07", ".08", ".09"]</var>
41 <var id="ZGRID">
42 (function() {
43 var zGrid = [];
44 for (var i = 0; i &lt; ROWS.length; i++) {
45 var zRow = [];
46 for (var j = 0; j &lt; COLUMNS.length; j++) {
47 zRow.push(zScores(roundTo(2,
48 (floorTo(0, ZSCORE) + i / 10 + j / 100) * 100)).toFixed(4));
49 }
50 zGrid.push(zRow);
51 }
52 return zGrid;
53 })()
54 </var>
55 <var id="ANSWER">ZGRID[ROW_INDEX][COL_INDEX]</var>
56 <var id="HEADER">"z"</var>
57 </div>
58 <div class="problem">
59 The scores on a statewide <var>course(1)</var> exam were normally distributed with
60 <code>\mu = <var>MEAN</var></code> and <code>\sigma = <var>STDDEV</var></code>.
61 <br /><var>person(1)</var> earned a<span data-if="floorTo(0, GRADE / 10) === 8">n</span>
62 <code><var>GRADE</var></code> on the exam.
63 </div>
64 <p class="question"><var>person(1)</var>'s exam grade was higher than what percentage
65 of test-takers? Use the cumulative z-table provided below. Round to two decimal places.</p>
66 <div class="fake_header reading">
67 <span><var>HEADER</var></span><span data-each="COLUMNS as i, column"><var>column</var></span>
68 </div>
69 <div class="fake_row reading" data-each="ROWS as i, row">
70 <span><var>row</var></span><span data-each="ZGRID[i] as j, zgrid"><var>zgrid</var></span>
71 </div>
5c60a281 » Gary Anderson
2012-10-03 Merge and squash pull request #31164 from saasmath/master
72 <div class="solution" data-inexact data-max-error="0.01" data-forms="percent">
9fdecffe » beneater
2012-04-16 Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
73 <span><var>roundTo(2, ANSWER * 100)</var></span>
74 </div>
e27b12ec » smenks13
2012-03-06 New exercise: Z-scores 2: Reading a z-table
75
9fdecffe » beneater
2012-04-16 Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
76 <div class="hints">
77 <p>
78 A cumulative z-table shows the probability that a standard normal variable will be
79 <b>less than</b> a certain value <b>(z)</b>.
80 </p>
81 <p>
82 In order to use the z-table, we first need to determine the
83 <span class="hint_blue">z-score</span> of <var>person( 1 )</var>'s exam grade.
84 </p>
85 <div>
86 <p>
87 Recall that we can calculate <var>his( 1 )</var> z-score by subtracting the
88 <span class="hint_pink">mean <code>(\mu)</code></span> from <var>his(1)</var>
89 grade and then dividing by the <span class="hint_green">standard deviation
90 <code>(\sigma)</code></span>.
91 </p>
92 <p>
93 <code>
94 \large{\quad z \quad = \quad
95 \dfrac{x - \pink{\mu}}{\green{\sigma}}
96 \quad = \quad \dfrac{<var>GRADE</var> - \pink{<var>MEAN</var>}}{\green{<var>STDDEV</var>}}
97 \quad = \quad <var>ZSCORE</var>}
98 </code>
99 </p>
100 </div>
101 <div>
102 <p>
103 Look up <code><var>ZSCORE</var></code> on the z-table. This value,
104 <code class="hint_blue"><var>ANSWER</var></code>, represents
105 the portion of the population that scored lower than
106 <code><var>GRADE</var></code> on the exam.
107 </p>
108 <div class="graphie">
109 var nth = ":nth-child(" + (COL_INDEX + 2) + ")";
110 $(".fake_row").eq(ROW_INDEX).find("span").css("background", ORANGE);
111 $(".fake_row span" + nth).css("background", ORANGE);
112 $(".fake_header span" + nth).css("background", ORANGE);
113 $(".fake_row").eq(ROW_INDEX).find("span" + nth).css("background", BLUE);
114 </div>
115 </div>
116 <p>
117 <var>person( 1 )</var> scored higher than
118 <code class="hint_blue"><var>roundTo(2, ANSWER * 100)</var>\%</code> of the
119 test-takers on the <var>course( 1 )</var> exam.
120 </p>
121 </div>
122 </div>
123 </div>
124 </div>
e27b12ec » smenks13
2012-03-06 New exercise: Z-scores 2: Reading a z-table
125 </body>
126 </html>
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