document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191023>Question 1191023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Data from a state indicate that scores on the SAT test are normally distributed with a mean of 1044 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.4. It is assumed that the two tests measure the same aptitude, but use different scales.\r<BR>\n" );
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document.write( "If a student gets an SAT score that is the 51 percentile, find the actual SAT score. Round answer to a whole number.\r<BR>\n" );
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document.write( "SAT score = \r<BR>\n" );
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document.write( "What would be the equivalent ACT score for this student? Round answer to 1 decimal place.\r<BR>\n" );
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document.write( "ACT score = \r<BR>\n" );
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document.write( "If a student gets an SAT score of 1451, find the equivalent ACT score. Round answer to 1 decimal place.\r<BR>\n" );
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document.write( "ACT score = <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 #822921 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "0.51 or 51st percentile is z=0.025<BR>\n" );
document.write( "z*sd=0.025*194=4.85=x-mean<BR>\n" );
document.write( "the score x for SAT is therefore 1048.85=1049<BR>\n" );
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document.write( "The ACT score is about 1/50 th of the SAT score, so the ACT score is going to change about 0.1<BR>\n" );
document.write( "z=0.025<BR>\n" );
document.write( "z*sd=0.11<BR>\n" );
document.write( "the ACT score will be 21.01 or 21.0<BR>\n" );
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document.write( "z=(1451-1044)/194=2.098<BR>\n" );
document.write( "for ACT, z*sd=9.23 or 9.2<BR>\n" );
document.write( "The ACT score will be 30.1<BR>\n" );
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