document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196282>Question 1196282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The middle 90% of the heights are between what two values? Round to one decimal place.\r<BR>\n" );
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document.write( "60.4 inches and 66.8 inches\r<BR>\n" );
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document.write( "59.5 inches and 67.7 inches\r<BR>\n" );
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document.write( "63.1 inches and 64.1 inches\r<BR>\n" );
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document.write( "61.9 inches and 65.3 inches\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829043 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = 63.6 = population mean<BR>\n" );
document.write( "sigma = 2.5 = population standard deviation\r<BR>\n" );
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document.write( "Since we're dealing with the middle 90%, each tail has an area of (1 - 0.9)/2 = 0.05<BR>\n" );
document.write( "Note that 0.05 + 0.90 + 0.05 = 1<BR>\n" );
document.write( "The area under the entire curve is always 1.\r<BR>\n" );
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document.write( "At 90% confidence, the z critical value is about 1.645<BR>\n" );
document.write( "Use a table like this to determine the critical value<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "Look blue row at the bottom marked \"Z\"<BR>\n" );
document.write( "The value 1.645 is just above the 90% confidence level \r<BR>\n" );
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document.write( "This means P(-1.645 < Z < 1.645) = 0.90 approximately<BR>\n" );
document.write( "Roughly 90% of the area under the standard normal curve is between -1.645 and 1.645\r<BR>\n" );
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document.write( "Let's find the raw score x that leads to z = -1.645<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "-1.645 = (x - 63.6)/2.5<BR>\n" );
document.write( "-1.645*2.5 = x - 63.6<BR>\n" );
document.write( "-4.1125 = x - 63.6<BR>\n" );
document.write( "x - 63.6 = -4.1125<BR>\n" );
document.write( "x = -4.1125 + 63.6<BR>\n" );
document.write( "x = 59.4875<BR>\n" );
document.write( "x = 59.5<BR>\n" );
document.write( "This is the approximate lower bound\r<BR>\n" );
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document.write( "Now repeat those steps with z = 1.645<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "1.645 = (x - 63.6)/2.5<BR>\n" );
document.write( "1.645*2.5 = x - 63.6<BR>\n" );
document.write( "4.1125 = x - 63.6<BR>\n" );
document.write( "x - 63.6 = 4.1125<BR>\n" );
document.write( "x = 4.1125 + 63.6<BR>\n" );
document.write( "x = 67.7125<BR>\n" );
document.write( "x = 67.7<BR>\n" );
document.write( "This is the approximate upper bound\r<BR>\n" );
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document.write( "Therefore, the middle 90% is between <font color=red>59.5 inches and 67.7 inches</font> which is <font color=red>choice B</font><BR>\n" );
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