document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=412386>Question 412386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I approach this question? Please help.\r<BR>\n" );
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document.write( "A dormitory has 1000 students' and you have determined that the average time in the shower is 10.0 minutes with a standard deviation of 2.0 minutes. The dean is considering automatic cutoffs of showers at 8 minutes. If he decides to do this, how many students will be affected?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #289657 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=289657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> normal distribution is assumed.<BR>\n" );
document.write( "mean is 10 minutes<BR>\n" );
document.write( "standard deviation is 2 minutes.\r<BR>\n" );
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document.write( "use of the David M. Lane z-score calculator will make this easy.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "In the top graph, enter a mean of 10 and a standard deviation of 2 and then click on the \"above\" box and enter 8.\r<BR>\n" );
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document.write( "The result is that 84.1345 percent of the students will be affected because those are the ones that require more than 8 minutes to finish their shower.\r<BR>\n" );
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document.write( "With a normal distribution, 50% of the scores are above the mean and 50% of the scores are below the mean.\r<BR>\n" );
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document.write( "If the dean cut off the shower at 10 minutes, 50% of the students would be affected.\r<BR>\n" );
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document.write( "Without knowing what tools you have at your disposal, it's difficult to give you an answer that suits your situation exactly.\r<BR>\n" );
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document.write( "If you are just using the z-score tables, then the derivation of the result is harder.\r<BR>\n" );
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document.write( "To use the tables, you need to convert the problem as given to a z-score.\r<BR>\n" );
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document.write( "The derivation of the z-score would make the mean equal to zero and the standard deviation equal to 1.\r<BR>\n" );
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document.write( "A score of 8 would then translate to an equivalent z-score.\r<BR>\n" );
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document.write( "Once you know that, you would then look up that value in the z-score table and look at the percentage of scores that would be to the right of that.\r<BR>\n" );
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document.write( "It's a lot messier, but can be done.\r<BR>\n" );
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document.write( "If you let me know what tools you have at your disposal, I can probably guide you to how to get the right answer.\r<BR>\n" );
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document.write( "The answer should be what I just showed you, regardless of the method you use.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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