document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281549>Question 281549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem is: A student scored 80 for an English exam and 72 for a History exam. If the class scores were normally distributed with a mean and standard deviation for English of 75 and 8 respectively, and for History 60 and 15 respectively, in which subject did the student achieve a higher standard, and what percentage of others achieved higher marks in each subject? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204541 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathematicians><B>Mathematicians(84)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathematicians><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=Mathematicians><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=204541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to find the Z score for each subject. You can recall, the higher z is, the smaller the graph goes which symbolize a higher tier in ranking. For a higher ranking, you want to take the greatest positive z\r<BR>\n" );
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document.write( "So, to calculate z score, you would calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28x+-+M%29%2Fs ALIGN=MIDDLE  ALT=\"z+=+%28x+-+M%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is the data, M is the mean, and s is standard deviation.\r<BR>\n" );
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document.write( "For English:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2880+-+75%29%2F8+=+5%2F8 ALIGN=MIDDLE  ALT=\"%2880+-+75%29%2F8+=+5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For History:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2872+-+60%29+%2F+15+=+12%2F15+=+4%2F5 ALIGN=MIDDLE  ALT=\"%2872+-+60%29+%2F+15+=+12%2F15+=+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F5+%3E+5%2F8 ALIGN=MIDDLE  ALT=\"+4%2F5+%3E+5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > => History achieved higher standard.\r<BR>\n" );
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document.write( "Now we need to find what percentage of others achieved higher marks in each subject. Unfortunately Z tables calculate Z values different and for that I cannot tell you how to use a Z table. \r<BR>\n" );
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document.write( "We calculated Z = 5/8 for English\r<BR>\n" );
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document.write( "We want to find P(z > 5/8)\r<BR>\n" );
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document.write( "You may need to do .5 - P(z = 5/8) or 1 - P(z = 5/8) depending on your Z table\r<BR>\n" );
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document.write( "Same thing with history except:\r<BR>\n" );
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document.write( "You may need to do .5 - P(z = 4/5) or 1 - P(z = 4/5) depending on your Z table.\r<BR>\n" );
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document.write( "Good luck! </SPAN>\n" );
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