document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918117>Question 918117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that test scores in a math class are normally distributed with a mean of 72 and a standard deviation of 12.5. What score would a student need in order to be at the 90th percentile for that test?\r<BR>\n" );
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document.write( "I understood how to solve this problem until the 90th percentile, what does this mean exactly. can I not just find the z score from the (z-mean)/std? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556907 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=556907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to find the z-score associated with the 90th percentile.<BR>\n" );
document.write( "then you need to translate that z-score into a raw score.<BR>\n" );
document.write( "the 90th percentile means that 90% of the people who take the test will have scores less than you.<BR>\n" );
document.write( "in the z-score table you look for a z-score of .90 because that is the area to the left of the z-score indicated.<BR>\n" );
document.write( "looking into the z-score table at <a  rel=nofollow HREF= \"https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf\" target = \"_blank\">https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf</a>, i find that an area of .90 equates to a z-score of somewhere between 1.28 and 1.29. <BR>\n" );
document.write( "a z-score of 1.28 has an area of .89973 to the left of it.<BR>\n" );
document.write( "a z-score of 1.29 has an area of .90147 to the left of it.<BR>\n" );
document.write( "a z-score of 1.28 is closer to the area of .90 so we'll go with that.<BR>\n" );
document.write( "you can use a calculator or you can interpolate to get closer, but it's usually not necessary to get that accurate.<BR>\n" );
document.write( "for example, my T-84 calculator says that the z-score associated with an area of .90 to the left of it is equal to 1.281551567.<BR>\n" );
document.write( "this is clearly closer to 1.28 than to 1.29.<BR>\n" );
document.write( "normally, when you use the z-score tables, the z-scores will be 2 decimal places so, for practical purposes, you round the z-score to the nearest 2 decimal places and you should be ok unless greater accuracy is required.\r<BR>\n" );
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document.write( "now that you know the z-score is 1.28, you have to translate that z-score to a raw score.\r<BR>\n" );
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document.write( "the mean of the test is 72 and the standard deviation is 12.5\r<BR>\n" );
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document.write( "the formula for z-score is:\r<BR>\n" );
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document.write( "z-score = (raw score - mean) / standard deviation\r<BR>\n" );
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document.write( "put in what you know and solve for what you don't know.\r<BR>\n" );
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document.write( "you know:\r<BR>\n" );
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document.write( "1.28 = (raw score - 72) / 12.5\r<BR>\n" );
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document.write( "solve for raw score as follows:\r<BR>\n" );
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document.write( "multiply both sides of the equation by 12.5 to get:<BR>\n" );
document.write( "12.5 * 1.28 = raw score - 72\r<BR>\n" );
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document.write( "add 72 to both sides of the equation to get:<BR>\n" );
document.write( "12.5 * 1.28 + 72 = raw score.\r<BR>\n" );
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document.write( "this leads to a raw score of 88.\r<BR>\n" );
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document.write( "if the mean is 72 and the standard deviation is 12.5, then a raw score of 88 will be better than approximately 90% of the population taking the test.\r<BR>\n" );
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document.write( "to confirm you're right, calculate the z-score and then find the area on the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "z-score = (88 - 72) / 12.5 = 1.28\r<BR>\n" );
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document.write( "area tot the left of z score of 1.28 = .89973 which is about as close to .90 as you can get without interpolating or using a calculator.\r<BR>\n" );
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document.write( "graphically, this would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/102901.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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