document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471570>Question 471570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let z be a random variable with a standard normal distribution. Find the indicated probability. P(z< -2.18)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323450 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to use a table to solve this problem. Tables are usually given at the back of the book.\r<BR>\n" );
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document.write( "<font size=6><b>Standard Normal Probability Table:</b></font>\r<BR>\n" );
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document.write( "The table shows the area to the left of a z-score (area shown in red)<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/z_left_tail_small.png\">\r<BR>\n" );
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document.write( "Now use the table to find the area to the left of -2.18 (it's shown in green and red below)\r<BR>\n" );
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document.write( "<th>z</th><th>0.00</th><th>0.01</th><th>0.02</th><th>0.03</th><th>0.04</th><th>0.05</th><th>0.06</th><th>0.07</th><th><font color=green>0.08</font></th><th>0.09</th><tr><TD ><b>-3.4</b></TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0003</TD><TD >0.0002</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-3.3</b></TD><TD >0.0005</TD><TD >0.0005</TD><TD >0.0005</TD><TD >0.0004</TD><TD >0.0004</TD><TD >0.0004</TD><TD >0.0004</TD><TD >0.0004</TD><TD >0.0004</TD><TD >0.0003</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-3.2</b></TD><TD >0.0007</TD><TD >0.0007</TD><TD >0.0006</TD><TD >0.0006</TD><TD >0.0006</TD><TD >0.0006</TD><TD >0.0006</TD><TD >0.0005</TD><TD >0.0005</TD><TD >0.0005</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-3.1</b></TD><TD >0.0010</TD><TD >0.0009</TD><TD >0.0009</TD><TD >0.0009</TD><TD >0.0008</TD><TD >0.0008</TD><TD >0.0008</TD><TD >0.0008</TD><TD >0.0007</TD><TD >0.0007</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-3.0</b></TD><TD >0.0013</TD><TD >0.0013</TD><TD >0.0013</TD><TD >0.0012</TD><TD >0.0012</TD><TD >0.0011</TD><TD >0.0011</TD><TD >0.0011</TD><TD >0.0010</TD><TD >0.0010</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.9</b></TD><TD >0.0019</TD><TD >0.0018</TD><TD >0.0018</TD><TD >0.0017</TD><TD >0.0016</TD><TD >0.0016</TD><TD >0.0015</TD><TD >0.0015</TD><TD >0.0014</TD><TD >0.0014</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.8</b></TD><TD >0.0026</TD><TD >0.0025</TD><TD >0.0024</TD><TD >0.0023</TD><TD >0.0023</TD><TD >0.0022</TD><TD >0.0021</TD><TD >0.0021</TD><TD >0.0020</TD><TD >0.0019</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.7</b></TD><TD >0.0035</TD><TD >0.0034</TD><TD >0.0033</TD><TD >0.0032</TD><TD >0.0031</TD><TD >0.0030</TD><TD >0.0029</TD><TD >0.0028</TD><TD >0.0027</TD><TD >0.0026</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.6</b></TD><TD >0.0047</TD><TD >0.0045</TD><TD >0.0044</TD><TD >0.0043</TD><TD >0.0041</TD><TD >0.0040</TD><TD >0.0039</TD><TD >0.0038</TD><TD >0.0037</TD><TD >0.0036</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.5</b></TD><TD >0.0062</TD><TD >0.0060</TD><TD >0.0059</TD><TD >0.0057</TD><TD >0.0055</TD><TD >0.0054</TD><TD >0.0052</TD><TD >0.0051</TD><TD >0.0049</TD><TD >0.0048</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.4</b></TD><TD >0.0082</TD><TD >0.0080</TD><TD >0.0078</TD><TD >0.0075</TD><TD >0.0073</TD><TD >0.0071</TD><TD >0.0069</TD><TD >0.0068</TD><TD >0.0066</TD><TD >0.0064</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.3</b></TD><TD >0.0107</TD><TD >0.0104</TD><TD >0.0102</TD><TD >0.0099</TD><TD >0.0096</TD><TD >0.0094</TD><TD >0.0091</TD><TD >0.0089</TD><TD >0.0087</TD><TD >0.0084</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.2</b></TD><TD >0.0139</TD><TD >0.0136</TD><TD >0.0132</TD><TD >0.0129</TD><TD >0.0125</TD><TD >0.0122</TD><TD >0.0119</TD><TD >0.0116</TD><TD >0.0113</TD><TD >0.0110</TD></tr>\r\n" );
document.write( "<tr><TD ><font color=green><b>-2.1</b></font></TD><TD >0.0179</TD><TD >0.0174</TD><TD >0.0170</TD><TD >0.0166</TD><TD >0.0162</TD><TD >0.0158</TD><TD >0.0154</TD><TD >0.0150</TD><TD ><font color=red><b>0.0146</b></font></TD><TD >0.0143</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-2.0</b></TD><TD >0.0228</TD><TD >0.0222</TD><TD >0.0217</TD><TD >0.0212</TD><TD >0.0207</TD><TD >0.0202</TD><TD >0.0197</TD><TD >0.0192</TD><TD >0.0188</TD><TD >0.0183</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.9</b></TD><TD >0.0287</TD><TD >0.0281</TD><TD >0.0274</TD><TD >0.0268</TD><TD >0.0262</TD><TD >0.0256</TD><TD > 0.0250</TD><TD >0.0244</TD><TD >0.0239</TD><TD >0.0233</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.8</b></TD><TD >0.0359</TD><TD >0.0351</TD><TD >0.0344</TD><TD >0.0336</TD><TD >0.0329</TD><TD >0.0322</TD><TD >0.0314</TD><TD >0.0307</TD><TD >0.0301</TD><TD >0.0294</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.7</b></TD><TD >0.0446</TD><TD >0.0436</TD><TD >0.0427</TD><TD >0.0418</TD><TD >0.0409</TD><TD >0.0401</TD><TD >0.0392</TD><TD >0.0384</TD><TD >0.0375</TD><TD >0.0367</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.6</b></TD><TD >0.0548</TD><TD >0.0537</TD><TD >0.0526</TD><TD >0.0516</TD><TD >0.0505</TD><TD >0.0495</TD><TD >0.0485</TD><TD >0.0475</TD><TD >0.0465</TD><TD >0.0455</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.5</b></TD><TD >0.0668</TD><TD >0.0655</TD><TD >0.0643</TD><TD >0.0630</TD><TD >0.0618</TD><TD >0.0606</TD><TD >0.0594</TD><TD >0.0582</TD><TD >0.0571</TD><TD >0.0559</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.4</b></TD><TD >0.0808</TD><TD >0.0793</TD><TD >0.0778</TD><TD >0.0764</TD><TD >0.0749</TD><TD >0.0735</TD><TD >0.0721</TD><TD >0.0708</TD><TD >0.0694</TD><TD >0.0681</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.3</b></TD><TD >0.0968</TD><TD >0.0951</TD><TD >0.0934</TD><TD >0.0918</TD><TD >0.0901</TD><TD >0.0885</TD><TD >0.0869</TD><TD >0.0853</TD><TD >0.0838</TD><TD >0.0823</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.2</b></TD><TD >0.1151</TD><TD >0.1131</TD><TD >0.1112</TD><TD >0.1093</TD><TD >0.1075</TD><TD >0.1056</TD><TD >0.1038</TD><TD >0.1020</TD><TD >0.1003</TD><TD >0.0985</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.1</b></TD><TD >0.1357</TD><TD >0.1335</TD><TD >0.1314</TD><TD >0.1292</TD><TD >0.1271</TD><TD >0.1251</TD><TD >0.1230</TD><TD >0.1210</TD><TD >0.1190</TD><TD >0.1170</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-1.0</b></TD><TD >0.1587</TD><TD >0.1562</TD><TD >0.1539</TD><TD >0.1515</TD><TD >0.1492</TD><TD >0.1469</TD><TD >0.1446</TD><TD >0.1423</TD><TD >0.1401</TD><TD >0.1379</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.9</b></TD><TD >0.1841</TD><TD >0.1814</TD><TD >0.1788</TD><TD >0.1762</TD><TD >0.1736</TD><TD >0.1711</TD><TD >0.1685</TD><TD >0.1660</TD><TD >0.1635</TD><TD >0.1611</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.8</b></TD><TD >0.2119</TD><TD >0.2090</TD><TD >0.2061</TD><TD >0.2033</TD><TD >0.2005</TD><TD >0.1977</TD><TD >0.1949</TD><TD >0.1922</TD><TD >0.1894</TD><TD >0.1867</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.7</b></TD><TD >0.2420</TD><TD >0.2389</TD><TD >0.2358</TD><TD >0.2327</TD><TD >0.2296</TD><TD >0.2266</TD><TD >0.2236</TD><TD >0.2206</TD><TD >0.2177</TD><TD >0.2148</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.6</b></TD><TD >0.2743</TD><TD >0.2709</TD><TD >0.2676</TD><TD >0.2643</TD><TD >0.2611</TD><TD >0.2578</TD><TD >0.2546</TD><TD >0.2514</TD><TD >0.2483</TD><TD >0.2451</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.5</b></TD><TD >0.3085</TD><TD >0.3050</TD><TD >0.3015</TD><TD >0.2981</TD><TD >0.2946</TD><TD >0.2912</TD><TD >0.2877</TD><TD >0.2843</TD><TD >0.2810</TD><TD >0.2776</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.4</b></TD><TD >0.3446</TD><TD >0.3409</TD><TD >0.3372</TD><TD >0.3336</TD><TD >0.3300</TD><TD >0.3264</TD><TD >0.3228</TD><TD >0.3192</TD><TD >0.3156</TD><TD >0.3121</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.3</b></TD><TD >0.3821</TD><TD >0.3783</TD><TD >0.3745</TD><TD >0.3707</TD><TD >0.3669</TD><TD >0.3632</TD><TD >0.3594</TD><TD >0.3557</TD><TD >0.3520</TD><TD >0.3483</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.2</b></TD><TD >0.4207</TD><TD >0.4168</TD><TD >0.4129</TD><TD >0.4090</TD><TD >0.4052</TD><TD >0.4013</TD><TD >0.3974</TD><TD >0.3936</TD><TD >0.3897</TD><TD >0.3859</TD></tr>\r\n" );
document.write( "<tr><TD ><b>-0.1</b></TD><TD >0.4602</TD><TD >0.4562</TD><TD >0.4522</TD><TD >0.4483</TD><TD >0.4443</TD><TD >0.4404</TD><TD >0.4364</TD><TD >0.4325</TD><TD >0.4286</TD><TD >0.4247</TD></tr>\r\n" );
document.write( "<tr><TD ><b>0.0</b></TD><TD >0.5000</TD><TD >0.4960</TD><TD >0.4920</TD><TD >0.4880</TD><TD >0.4840</TD><TD >0.4801</TD><TD >0.4761</TD><TD >0.4721</TD><TD >0.4681</TD><TD >0.4641</TD></tr>\r\n" );
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document.write( "From the table, we see that the area to the left of z = -2.18 is 0.0146\r<BR>\n" );
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document.write( "So P(z< -2.18) = 0.0146 </SPAN>\n" );
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