document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194419>Question 1194419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following exam grades has a better relative position?<BR>\n" );
document.write( "a.) A grade of 43 on a algebra test with x̄=40 and s=3<BR>\n" );
document.write( "b.) A grade of 75 on a geometry test with x̄=72 and s=5\r<BR>\n" );
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document.write( "Show full solution, thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826618 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=826618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The z score formula is<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "x = raw score<BR>\n" );
document.write( "mu = mean<BR>\n" );
document.write( "sigma = standard deviation\r<BR>\n" );
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document.write( "I'll treat each xbar as mu, and each s as sigma\r<BR>\n" );
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document.write( "For part A, we have<BR>\n" );
document.write( "x = 43<BR>\n" );
document.write( "mu = 40<BR>\n" );
document.write( "sigma = 3\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (43-40)/3<BR>\n" );
document.write( "z = 3/3<BR>\n" );
document.write( "z = 1<BR>\n" );
document.write( "which is the z score to part A.\r<BR>\n" );
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document.write( "A z score of 1 means we're exactly 1 standard deviation above the mean.<BR>\n" );
document.write( "Positive z scores are above the mean, while negative z scores are below the mean.\r<BR>\n" );
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document.write( "For part B, we have this z score<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (75 - 72)/5<BR>\n" );
document.write( "z = 3/5<BR>\n" );
document.write( "z = 0.6\r<BR>\n" );
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document.write( "We can see that the z score in part A is larger; therefore, the exam grade in class A is in a better relative position to the entire class.\r<BR>\n" );
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document.write( "Answer: Choice A.<BR>\n" );
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document.write( " </SPAN>\n" );
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