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553 lines
13 KiB
HTML
553 lines
13 KiB
HTML
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<title>Standard Normal Distribution Table</title>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Standard Normal Distribution Table</h1>
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<div class="script" style="height:400px">
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images/normal-dist.js
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</div>
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<p class="center"><span class="larger">This is the "bell-shaped" curve of the Standard Normal Distribution.</span><br>
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<span class="center">It is a <a href="standard-normal-distribution.html">Normal Distribution</a> with mean 0 and <a href="standard-deviation.html" target="_blank">standard deviation</a> 1.</span></p>
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<p>It shows you the percent of population:</p>
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<ul>
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<li>between 0 and Z (option "0 to Z")</li>
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<li>less than Z (option "Up to Z")</li>
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<li>greater than Z (option "Z onwards")</li>
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</ul>
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<p>It only display values to 0.01%</p>
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<h2>The Table</h2>
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<p>You can also use the table below. The table shows the area from 0 to Z.</p>
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<p>Instead of one LONG table, we have put the "<b>0.1</b>"s running down, then the "<b>0.01</b>"s running along. (Example of how to use is below)</p>
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<div class="simple">
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<table align="center" width="450" cellspacing="2" cellpadding="3" border="0">
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<tbody>
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<tr>
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<th align="center"><font style=" text-align:center;" class="larger">Z</font></th>
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<th>0.00</th>
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<th>0.01</th>
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<th>0.02</th>
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<th>0.03</th>
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<th>0.04</th>
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<th>0.05</th>
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<th>0.06</th>
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<th>0.07</th>
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<th>0.08</th>
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<th>0.09</th>
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</tr>
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<tr>
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<th>0.0</th>
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<td>0.0000</td>
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<td>0.0040</td>
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<td>0.0080</td>
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<td>0.0120</td>
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<td>0.0160</td>
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<td>0.0199</td>
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<td>0.0239</td>
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<td>0.0279</td>
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<td>0.0319</td>
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<td>0.0359</td>
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</tr>
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<tr>
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<th>0.1</th>
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<td>0.0398</td>
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<td>0.0438</td>
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<td>0.0478</td>
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<td>0.0517</td>
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<td>0.0557</td>
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<td>0.0596</td>
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<td>0.0636</td>
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<td>0.0675</td>
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<td>0.0714</td>
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<td>0.0753</td>
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</tr>
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<tr>
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<th>0.2</th>
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<td>0.0793</td>
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<td>0.0832</td>
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<td>0.0871</td>
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<td>0.0910</td>
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<td>0.0948</td>
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<td>0.0987</td>
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<td>0.1026</td>
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<td>0.1064</td>
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<td>0.1103</td>
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<td>0.1141</td>
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</tr>
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<tr>
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<th>0.3</th>
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<td>0.1179</td>
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<td>0.1217</td>
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<td>0.1255</td>
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<td>0.1293</td>
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<td>0.1331</td>
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<td>0.1368</td>
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<td>0.1406</td>
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<td>0.1443</td>
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<td>0.1480</td>
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<td>0.1517</td>
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</tr>
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<tr>
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<th>0.4</th>
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<td>0.1554</td>
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<td>0.1591</td>
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<td>0.1628</td>
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<td>0.1664</td>
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<td>0.1700</td>
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<td>0.1736</td>
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<td>0.1772</td>
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<td>0.1808</td>
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<td>0.1844</td>
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<td>0.1879</td>
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</tr>
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<tr>
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<th>0.5</th>
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<td>0.1915</td>
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<td>0.1950</td>
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<td>0.1985</td>
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<td>0.2019</td>
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<td>0.2054</td>
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<td>0.2088</td>
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<td>0.2123</td>
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<td>0.2157</td>
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<td>0.2190</td>
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<td>0.2224</td>
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</tr>
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<tr>
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<th>0.6</th>
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<td>0.2257</td>
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<td>0.2291</td>
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<td>0.2324</td>
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<td>0.2357</td>
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<td>0.2389</td>
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<td>0.2422</td>
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<td>0.2454</td>
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<td>0.2486</td>
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<td>0.2517</td>
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<td>0.2549</td>
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</tr>
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<tr>
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<th>0.7</th>
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<td>0.2580</td>
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<td>0.2611</td>
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<td>0.2642</td>
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<td>0.2673</td>
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<td>0.2704</td>
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<td>0.2734</td>
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<td>0.2764</td>
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<td>0.2794</td>
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<td>0.2823</td>
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<td>0.2852</td>
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</tr>
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<tr>
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<th>0.8</th>
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<td>0.2881</td>
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<td>0.2910</td>
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<td>0.2939</td>
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<td>0.2967</td>
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<td>0.2995</td>
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<td>0.3023</td>
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<td>0.3051</td>
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<td>0.3078</td>
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<td>0.3106</td>
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<td>0.3133</td>
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</tr>
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<tr>
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<th>0.9</th>
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<td>0.3159</td>
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<td>0.3186</td>
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<td>0.3212</td>
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<td>0.3238</td>
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<td>0.3264</td>
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<td>0.3289</td>
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<td>0.3315</td>
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<td>0.3340</td>
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<td>0.3365</td>
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<td>0.3389</td>
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</tr>
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<tr>
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<th>1.0</th>
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<td>0.3413</td>
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<td>0.3438</td>
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<td>0.3461</td>
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<td>0.3485</td>
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<td>0.3508</td>
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<td>0.3531</td>
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<td>0.3554</td>
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<td>0.3577</td>
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<td>0.3599</td>
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<td>0.3621</td>
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</tr>
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<tr>
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<th>1.1</th>
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<td>0.3643</td>
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<td>0.3665</td>
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<td>0.3686</td>
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<td>0.3708</td>
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<td>0.3729</td>
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<td>0.3749</td>
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<td>0.3770</td>
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<td>0.3790</td>
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<td>0.3810</td>
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<td>0.3830</td>
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</tr>
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<tr>
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<th>1.2</th>
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<td>0.3849</td>
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<td>0.3869</td>
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<td>0.3888</td>
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<td>0.3907</td>
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<td>0.3925</td>
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<td>0.3944</td>
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<td>0.3962</td>
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<td>0.3980</td>
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<td>0.3997</td>
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<td>0.4015</td>
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</tr>
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<tr>
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<th>1.3</th>
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<td>0.4032</td>
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<td>0.4049</td>
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<td>0.4066</td>
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<td>0.4082</td>
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<td>0.4099</td>
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<td>0.4115</td>
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<td>0.4131</td>
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<td>0.4147</td>
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<td>0.4162</td>
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<td>0.4177</td>
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</tr>
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<tr>
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<th>1.4</th>
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<td>0.4192</td>
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<td>0.4207</td>
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<td>0.4222</td>
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<td>0.4236</td>
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<td>0.4251</td>
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<td>0.4265</td>
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<td>0.4279</td>
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<td>0.4292</td>
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<td>0.4306</td>
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<td>0.4319</td>
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</tr>
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<tr>
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<th>1.5</th>
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<td>0.4332</td>
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<td>0.4345</td>
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<td>0.4357</td>
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<td>0.4370</td>
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<td>0.4382</td>
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<td>0.4394</td>
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<td>0.4406</td>
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<td>0.4418</td>
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<td>0.4429</td>
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<td>0.4441</td>
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</tr>
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<tr>
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<th>1.6</th>
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<td>0.4452</td>
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<td>0.4463</td>
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<td>0.4474</td>
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<td>0.4484</td>
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<td>0.4495</td>
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<td>0.4505</td>
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<td>0.4515</td>
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<td>0.4525</td>
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<td>0.4535</td>
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<td>0.4545</td>
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</tr>
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<tr>
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<th>1.7</th>
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<td>0.4554</td>
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<td>0.4564</td>
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<td>0.4573</td>
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<td>0.4582</td>
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<td>0.4591</td>
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<td>0.4599</td>
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<td>0.4608</td>
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<td>0.4616</td>
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<td>0.4625</td>
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<td>0.4633</td>
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</tr>
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<tr>
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<th>1.8</th>
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<td>0.4641</td>
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<td>0.4649</td>
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<td>0.4656</td>
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<td>0.4664</td>
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<td>0.4671</td>
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<td>0.4678</td>
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<td>0.4686</td>
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<td>0.4693</td>
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<td>0.4699</td>
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<td>0.4706</td>
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</tr>
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<tr>
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<th>1.9</th>
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<td>0.4713</td>
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<td>0.4719</td>
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<td>0.4726</td>
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<td>0.4732</td>
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<td>0.4738</td>
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<td>0.4744</td>
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<td>0.4750</td>
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<td>0.4756</td>
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<td>0.4761</td>
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<td>0.4767</td>
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</tr>
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<tr>
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<th>2.0</th>
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<td>0.4772</td>
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<td>0.4778</td>
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<td>0.4783</td>
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<td>0.4788</td>
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<td>0.4793</td>
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<td>0.4798</td>
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<td>0.4803</td>
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<td>0.4808</td>
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<td>0.4812</td>
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<td>0.4817</td>
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</tr>
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<tr>
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<th>2.1</th>
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<td>0.4821</td>
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<td>0.4826</td>
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<td>0.4830</td>
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<td>0.4834</td>
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<td>0.4838</td>
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<td>0.4842</td>
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<td>0.4846</td>
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<td>0.4850</td>
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<td>0.4854</td>
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<td>0.4857</td>
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</tr>
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<tr>
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<th>2.2</th>
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<td>0.4861</td>
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<td>0.4864</td>
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<td>0.4868</td>
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<td>0.4871</td>
|
||
<td>0.4875</td>
|
||
<td>0.4878</td>
|
||
<td>0.4881</td>
|
||
<td>0.4884</td>
|
||
<td>0.4887</td>
|
||
<td>0.4890</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.3</th>
|
||
<td>0.4893</td>
|
||
<td>0.4896</td>
|
||
<td>0.4898</td>
|
||
<td>0.4901</td>
|
||
<td>0.4904</td>
|
||
<td>0.4906</td>
|
||
<td>0.4909</td>
|
||
<td>0.4911</td>
|
||
<td>0.4913</td>
|
||
<td>0.4916</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.4</th>
|
||
<td>0.4918</td>
|
||
<td>0.4920</td>
|
||
<td>0.4922</td>
|
||
<td>0.4925</td>
|
||
<td>0.4927</td>
|
||
<td>0.4929</td>
|
||
<td>0.4931</td>
|
||
<td>0.4932</td>
|
||
<td>0.4934</td>
|
||
<td>0.4936</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.5</th>
|
||
<td>0.4938</td>
|
||
<td>0.4940</td>
|
||
<td>0.4941</td>
|
||
<td>0.4943</td>
|
||
<td>0.4945</td>
|
||
<td>0.4946</td>
|
||
<td>0.4948</td>
|
||
<td>0.4949</td>
|
||
<td>0.4951</td>
|
||
<td>0.4952</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.6</th>
|
||
<td>0.4953</td>
|
||
<td>0.4955</td>
|
||
<td>0.4956</td>
|
||
<td>0.4957</td>
|
||
<td>0.4959</td>
|
||
<td>0.4960</td>
|
||
<td>0.4961</td>
|
||
<td>0.4962</td>
|
||
<td>0.4963</td>
|
||
<td>0.4964</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.7</th>
|
||
<td>0.4965</td>
|
||
<td>0.4966</td>
|
||
<td>0.4967</td>
|
||
<td>0.4968</td>
|
||
<td>0.4969</td>
|
||
<td>0.4970</td>
|
||
<td>0.4971</td>
|
||
<td>0.4972</td>
|
||
<td>0.4973</td>
|
||
<td>0.4974</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.8</th>
|
||
<td>0.4974</td>
|
||
<td>0.4975</td>
|
||
<td>0.4976</td>
|
||
<td>0.4977</td>
|
||
<td>0.4977</td>
|
||
<td>0.4978</td>
|
||
<td>0.4979</td>
|
||
<td>0.4979</td>
|
||
<td>0.4980</td>
|
||
<td>0.4981</td>
|
||
</tr>
|
||
<tr>
|
||
<th>2.9</th>
|
||
<td>0.4981</td>
|
||
<td>0.4982</td>
|
||
<td>0.4982</td>
|
||
<td>0.4983</td>
|
||
<td>0.4984</td>
|
||
<td>0.4984</td>
|
||
<td>0.4985</td>
|
||
<td>0.4985</td>
|
||
<td>0.4986</td>
|
||
<td>0.4986</td>
|
||
</tr>
|
||
<tr>
|
||
<th>3.0</th>
|
||
<td>0.4987</td>
|
||
<td>0.4987</td>
|
||
<td>0.4987</td>
|
||
<td>0.4988</td>
|
||
<td>0.4988</td>
|
||
<td>0.4989</td>
|
||
<td>0.4989</td>
|
||
<td>0.4989</td>
|
||
<td>0.4990</td>
|
||
<td>0.4990</td>
|
||
</tr>
|
||
</tbody></table>
|
||
</div>
|
||
<p> </p>
|
||
|
||
<div class="example">
|
||
<h3>Example: Percent of Population Between 0 and 0.45</h3>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/standard-normal-distribution-0-45.svg" alt="standard normal distribution 0.45 = 0.1736" style="width:299px; height:159px; min-width:299px;" ></p><p>Start at the row for 0.4, and read along
|
||
until 0.45: there is the value 0.1736</p>
|
||
<p>And 0.1736 is <b>17.36%</b></p>
|
||
<p>So 17.36% of the population are between 0 and 0.45 Standard Deviations from the Mean.</p>
|
||
</div>
|
||
<p>Because the curve is symmetrical, the same table can be used for values going either direction, so a negative
|
||
0.45 also has an area of 0.1736</p>
|
||
<div class="example">
|
||
<h3>Example: Percent of Population Z Between −1 and 2</h3>
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/standard-normal-distribution-1-2.svg" alt="standard normal distribution -1 to +2" style="width:299px; height:143px; min-width:299px;" ></p>
|
||
<p>From <b>−1 to 0</b> is the same as from <b>0 to +1</b>:</p>
|
||
<p class="center">At the row for 1.0, first column 1.00, there is the value <b>0.3413</b></p>
|
||
<p>From <b>0 to +2</b> is:</p>
|
||
<p class="center">At the row for 2.0, first column 2.00, there is the value <b>0.4772</b></p>
|
||
<p>Add the two to get the total between −1 and 2:</p>
|
||
<p class="center">0.3413 + 0.4772 = <b>0.8185</b></p>
|
||
<p>And <b>0.8185</b> is <b>81.85%</b></p>
|
||
<p>So 81.85% of the population are between −1 and +2 Standard Deviations from the Mean.</p>
|
||
</div>
|
||
|
||
<p> </p>
|
||
<div class="questions">1486, 1487, 1488, 1489, 1490, 1491, 3846, 3847, 3848, 3849</div>
|
||
|
||
<div class="related">
|
||
<a href="standard-normal-distribution.html">Normal Distribution</a>
|
||
<a href="standard-deviation.html">Standard Deviation</a>
|
||
<a href="quincunx.html">Quincunx</a>
|
||
<a href="index.html">Probability and Statistics Menu</a>
|
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