document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171969>Question 1171969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A psychologist finds that the intelligence quotients of a group of patients are<BR>\n" );
document.write( "normally distributed, with a mean of 102 and a standard deviation of 16. Find<BR>\n" );
document.write( "the percent of the patients with IQs<BR>\n" );
document.write( "a) above 114.<BR>\n" );
document.write( "b) between 90 and 118.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797056 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>a) above 114</i><BR>\n" );
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document.write( "z-score = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28114-102%29%2F16 ALIGN=MIDDLE  ALT=\"%28114-102%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F16 ALIGN=MIDDLE  ALT=\"12%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.75<BR>\n" );
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document.write( "A z-score of 0.75 is 0.7734.  This means 77.34% of patients have an IQ below 114.  To find the percentage of people with IQs above 114, subtract this from 1. This result is 22.66%. <b>Therefore, 22.66% of patients have an IQ above 114.</b><BR>\n" );
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document.write( "<i>b) between 90 and 118</i><BR>\n" );
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document.write( "z-score1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28118-102%29%2F16 ALIGN=MIDDLE  ALT=\"%28118-102%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F16 ALIGN=MIDDLE  ALT=\"16%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.00<BR>\n" );
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document.write( "A z-score of 1.00 is 0.8413. This means 84.13% of patients have an IQ below 118.<BR>\n" );
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document.write( "z-score2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2890-102%29%2F16 ALIGN=MIDDLE  ALT=\"%2890-102%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%2F16 ALIGN=MIDDLE  ALT=\"%28-12%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -0.75<BR>\n" );
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document.write( "A z-score of -0.75 is 0.2266. This means 22.66% of patients have an IQ below 90.<BR>\n" );
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document.write( "To find the percentage of patients with IQs between 90 and 118, subtract 22.66% from 84.13%. This result is 61.47%.  <b>Therefore, 61.47% of the patients have an IQ between 90 and 118.</b> </SPAN>\n" );
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