document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150424>Question 1150424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the heights of adult women in the United States are normally distributed with a mean of 63.5 inches and a standard deviation of 2.3 inches. Jennifer is taller than 90% of the population of U.S. women. How tall (in inches) is Jennifer? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774169 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=774169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 63.5 inches<BR>\n" );
document.write( "standard deviation = 2.3 inches.<BR>\n" );
document.write( "jennifer is taller than 90% of the population of u.s. women.<BR>\n" );
document.write( "how tall, in inches, is jennifer.<BR>\n" );
document.write( "you can use the following calculator to solve this.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "i did 3 calculations as shown below:\r<BR>\n" );
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document.write( "you put in the mean of 63.5 and the standard deviation of 2.3\r<BR>\n" );
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document.write( "the first display finds the raw score that has an area of .10 under the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "the second display finds the area to the right of the raw score.\r<BR>\n" );
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document.write( "you can also work this from z-scores.\r<BR>\n" );
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document.write( "first find the z-score that has 10% of the area under the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "using my ti-84 plus, i find that the z-score is 1.281551567 which can be rounded to 1.281551.\r<BR>\n" );
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document.write( "you then look for the area under the normal distribution curve to the right of that z-score to confirm this is accurate.\r<BR>\n" );
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document.write( "here's a display of that.<BR>\n" );
document.write( "the mean is 0 and the standard is 1 when working with the z-score.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/020806.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "to find the raw score, use the z-score formula of z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "s is the standard deviation, in this case.\r<BR>\n" );
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document.write( "formula becomes 1.281551 = (x - 63.5) / 2.3<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1.281551 * 2.3 + 63.5 = 66.4475 which can be rounded to 66.4.\r<BR>\n" );
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document.write( "as seen on the graph, the area to the right of that is .10.<BR>\n" );
document.write( "the area to the left of that is 1 - .10 = .90.<BR>\n" );
document.write( "that means that jennifer's height is greater than 90% of the group of girls whose mean height is 63.5 inches and whose standard deviation is 2.3 inches.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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