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e27b12e @smenks13 New exercise: Z-scores 2: Reading a z-table
smenks13 authored
1 <!DOCTYPE html>
aa6f903 @xymostech Replace toFixed with localeToFixed
xymostech authored
2 <html data-require="math math-format graphie word-problems stat">
ced362c @jeresig Run the exercise cleaner.
jeresig authored
3 <head>
4 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
24b734a @jeresig Clean up the titles of the HTML files.
jeresig authored
5 <title>Z scores 2</title>
ac1415e @spicyj Use requirejs for module loading
spicyj authored
6 <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
e27b12e @smenks13 New exercise: Z-scores 2: Reading a z-table
smenks13 authored
7 </head>
8 <body>
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
9 <div class="exercise">
10 <div class="problems">
87b4394 @beneater Fix a bunch of nits from math questions feedback
beneater authored
11 <div data-calculator="">
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
12 <div class="vars">
13 <var id="COL_INDEX">randRange(0, 9)</var>
14 <var id="ROW_INDEX">randRange(0, 9)</var>
15 <var id="ZSCORE">roundTo(2, randRange(0, 2) + ROW_INDEX / 10 + COL_INDEX / 100)</var>
16 <var id="GRADE">randRange(70, 90)</var>
17 <var id="STDDEV">randRange(2, 6)</var>
d5bdea4 use localized decimals and fix #76166
maik authored
18 <var id="MEAN">localeToFixed(GRADE - ZSCORE * STDDEV, 2)</var>
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
19 <var id="ROWS">
20 (function() {
21 var rowNames = [];
22 for(var i = floorTo(0, ZSCORE); i &lt; (floorTo(0, ZSCORE) + 1); i += 0.1) {
aa6f903 @xymostech Replace toFixed with localeToFixed
xymostech authored
23 rowNames.push(localeToFixed(i, 1));
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
24 }
25 return rowNames;
26 })()
27 </var>
d5bdea4 use localized decimals and fix #76166
maik authored
28 <var id="COLUMNS">[.00, .01, .02, .03, .04, .05, .06, .07, .08, .09]</var>
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
29 <var id="ZGRID">
30 (function() {
31 var zGrid = [];
32 for (var i = 0; i &lt; ROWS.length; i++) {
33 var zRow = [];
34 for (var j = 0; j &lt; COLUMNS.length; j++) {
d5bdea4 use localized decimals and fix #76166
maik authored
35 zRow.push(zScores(roundTo(2,
36 (floorTo(0, ZSCORE) + i / 10 + j / 100) * 100)));
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
37 }
38 zGrid.push(zRow);
39 }
40 return zGrid;
41 })()
42 </var>
43 <var id="ANSWER">ZGRID[ROW_INDEX][COL_INDEX]</var>
44 <var id="HEADER">"z"</var>
45 </div>
46 <div class="problem">
47 The scores on a statewide <var>course(1)</var> exam were normally distributed with
48 <code>\mu = <var>MEAN</var></code> and <code>\sigma = <var>STDDEV</var></code>.
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
49 <br><var>person(1)</var> scored <code><var>GRADE</var></code> on the exam.
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
50 </div>
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
51 <p class="question">
35e1ca9 @xymostech Rearrange answer area content within some exercises
xymostech authored
52 <var>person(1)</var>'s exam grade was higher than what percentage of test-takers?</p>
53 <p class="render-answer-area-here"></p>
114a43c @ariabuckles lint
ariabuckles authored
54 <p>Use the cumulative z-table provided below.</p>
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
55 <div class="fake_header z-score-table">
d5bdea4 use localized decimals and fix #76166
maik authored
56 <span><var>HEADER</var></span><span data-each="COLUMNS as i, column"><var>localeToFixed(column, 2).substr(1)</var></span>
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
57 </div>
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
58 <div class="fake_row z-score-table" data-each="ROWS as i, row">
d5bdea4 use localized decimals and fix #76166
maik authored
59 <span><var>row</var></span><span data-each="ZGRID[i] as j, zgrid"><var>localeToFixed(zgrid, 4)</var></span>
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
60 </div>
9d0ccf7 @petercollingridge Move z-table styles to external file and allow for answers 0.0001 out
petercollingridge authored
61 <div class="solution" data-forms="integer, proper, improper, mixed, decimal, percent" data-simplify="optional" data-inexact="" data-max-error="0.0001">
62 <var>roundTo(4, ANSWER)</var>
63 </div>
e27b12e @smenks13 New exercise: Z-scores 2: Reading a z-table
smenks13 authored
64
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
65 <div class="hints">
66 <p>
67 A cumulative z-table shows the probability that a standard normal variable will be
68 <b>less than</b> a certain value <b>(z)</b>.
69 </p>
70 <p>
71 In order to use the z-table, we first need to determine the
72 <span class="hint_blue">z-score</span> of <var>person( 1 )</var>'s exam grade.
73 </p>
74 <div>
9de9147 @jeresig Add in a tool for automatically fixing some i18n issues in exercises. Ri...
jeresig authored
75 <p data-if="isMale(1)">
76 Recall that we can calculate his z-score by subtracting the
77 <span class="hint_pink">mean <code>(\mu)</code></span> from his
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
78 grade and then dividing by the <span class="hint_purple">standard deviation
9de9147 @jeresig Add in a tool for automatically fixing some i18n issues in exercises. Ri...
jeresig authored
79 <code>(\sigma)</code></span>.
80 </p><p data-else="">
81 Recall that we can calculate her z-score by subtracting the
82 <span class="hint_pink">mean <code>(\mu)</code></span> from her
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
83 grade and then dividing by the <span class="hint_purple">standard deviation
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
84 <code>(\sigma)</code></span>.
85 </p>
86 <p>
87 <code>
88 \large{\quad z \quad = \quad
08a4096 @petercollingridge Tweak question wording
petercollingridge authored
89 \dfrac{x - \pink{\mu}}{\purple{\sigma}}
90 \quad = \quad \dfrac{<var>GRADE</var> - \pink{<var>MEAN</var>}}{\purple{<var>STDDEV</var>}}
d5bdea4 use localized decimals and fix #76166
maik authored
91 \quad = \quad <var>localeToFixed(ZSCORE, 2)</var>}
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
92 </code>
93 </p>
94 </div>
95 <div>
96 <p>
d5bdea4 use localized decimals and fix #76166
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97 Look up <code><var>localeToFixed(ZSCORE, 2)</var></code> on the z-table. This value,
98 <code class="hint_blue"><var>localeToFixed(ANSWER, 4)</var></code>, represents
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
99 the portion of the population that scored lower than
100 <code><var>GRADE</var></code> on the exam.
101 </p>
102 <div class="graphie">
103 var nth = ":nth-child(" + (COL_INDEX + 2) + ")";
104 $(".fake_row").eq(ROW_INDEX).find("span").css("background", ORANGE);
105 $(".fake_row span" + nth).css("background", ORANGE);
106 $(".fake_header span" + nth).css("background", ORANGE);
107 $(".fake_row").eq(ROW_INDEX).find("span" + nth).css("background", BLUE);
108 </div>
109 </div>
110 <p>
111 <var>person( 1 )</var> scored higher than
d5bdea4 use localized decimals and fix #76166
maik authored
112 <code class="hint_blue"><var>localeToFixed(ANSWER * 100, 2)</var>\%</code> of the
9fdecff @beneater Merge branch 'zScore2' of https://github.com/smenks13/khan-exercises
beneater authored
113 test-takers on the <var>course( 1 )</var> exam.
114 </p>
115 </div>
116 </div>
117 </div>
118 </div>
ced362c @jeresig Run the exercise cleaner.
jeresig authored
119 </body>
120 </html>
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