document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=834023>Question 834023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Exam scores are normally distributed with a mean of 81 and a standard deviation of 9.\r<BR>\n" );
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document.write( "a) What is the minimum score one must have to be in the top 4% of the students taking the exam?\r<BR>\n" );
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document.write( "b) What percentage of scores are below 90?\r<BR>\n" );
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document.write( "c) What percentage of scores are above 45?\r<BR>\n" );
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document.write( "d) If 30 people take this exam, how many would you expect to get above a 93%?\r<BR>\n" );
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document.write( "e) If you have a test score in the 45th percentile, what is its z-score?\r<BR>\n" );
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document.write( "f) What is the z-score and percentile for an exam score 1.2 standard deviations below the mean? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502797 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=502797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Exam scores are normally distributed with a mean of 81 <BR>\n" );
document.write( "and a standard deviation of 9. <BR>\n" );
document.write( "a) What is the minimum score one must have to be in the top 4% of the students taking the exam?<BR>\n" );
document.write( "Find the z-score with a right tail of 4%:<BR>\n" );
document.write( "invNorm(0.96) = 1.7507<BR>\n" );
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document.write( "Find the corresponding score: 81+1.7507*9 = 96.76<BR>\n" );
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document.write( "b) What percentage of scores are below 90?<BR>\n" );
document.write( "z(90) = (90-81)/9 = 1<BR>\n" );
document.write( "P(x < 90) = P(z < 1) = 0.8413<BR>\n" );
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document.write( "c) What percentage of scores are above 45?<BR>\n" );
document.write( "Find z(45) then find the Probability z is above that z value.<BR>\n" );
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document.write( "d) If 30 people take this exam, how many would you expect to get above a 93%?<BR>\n" );
document.write( "Ans:0.07*30 = 2.1<BR>\n" );
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document.write( "e) If you have a test score in the 45th percentile, what is its z-score?<BR>\n" );
document.write( "invNorm(0.45) = -0.1257<BR>\n" );
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document.write( "f) What is the z-score and percentile for an exam score 1.2 standard deviations below the mean?<BR>\n" );
document.write( "z = -1.2<BR>\n" );
document.write( "score = 81-1.2*9 = 70.2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( " </SPAN>\n" );
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