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<!DOCTYPE html>
<html data-require="math word-problems">
<meta charset="UTF-8">
<title>Z scores 1</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
<div class="exercise">
<div class="problems">
<div id="original">
<div class="vars">
<var id="MEAN">randRange( 65, 85 )</var>
<var id="STDDEV">randRange( 2, 5 ) + randRange( 0, 1 ) * 0.5</var>
<var id="GRADE">randRangeWeighted( roundTo( 0, MEAN - STDDEV * 3 ), min( roundTo( 0, MEAN + STDDEV * 3 ), 100 ), MEAN, 0 )</var>
<var id="ZSCORE">roundTo( 2, ( GRADE - MEAN ) / STDDEV )</var>
<var id="SOLUTION">localeToFixed(ZSCORE, 2)</var>
<div class="problem">
The grades on a <var>course( 1 )</var> midterm at <var>school( 1 )</var> are normally distributed with <code>\mu = <var>MEAN</var></code> and <code>\sigma = <var>localeToFixed(STDDEV, 1)</var></code>.
<br><var>person( 1 )</var> scored <code><var>GRADE</var></code> on the exam.
<p class="question">Find the z-score for <var>person( 1 )</var>'s exam grade. Round to two decimal places.</p>
<div class="solution" data-inexact="" data-max-error="0.01"><var>(GRADE - MEAN) /STDDEV</var></div>
<div class="hints">
<p>A z-score is defined as the number of <span class="hint_green">standard deviations</span> a specific point is away from the <span class="hint_pink">mean</span>.</p>
<code>\large{\quad z \quad = \quad
\dfrac{<var>GRADE</var> - \pink{<var>MEAN</var>}}{\green{<var>localeToFixed(STDDEV, 1)</var>}}}</code>
<p><code>\large{\quad z \quad \approx \quad <var>SOLUTION</var>}</code></p>
The z-score is <code><var>localeToFixed(ZSCORE, 2)</var></code>.
<span data-if="isSingular(ZSCORE)">
In other words, <var>person(1)</var>'s score was <code><var>SOLUTION</var></code> standard deviation above the mean.
<span data-else-if="isSingular(-ZSCORE)">
In other words, <var>person(1)</var>'s score was <code><var>SOLUTION</var></code> standard deviation below the mean.
<span data-else-if="ZSCORE > 0">
In other words, <var>person(1)</var>'s score was <code><var>SOLUTION</var></code> standard deviations above the mean.
<span data-else="">
In other words, <var>person(1)</var>'s score was <code><var>SOLUTION</var></code> standard deviations below the mean.
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