document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141427>Question 1141427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Scores on a recent national statistics exam were normally distributed with a mean of 90 and a standard deviation of 5.<BR>\n" );
document.write( "1.What is the probability that a randomly selected exam will have a score of at least 85?<BR>\n" );
document.write( "2.What percentage of exams will have scores between 89 and 92?<BR>\n" );
document.write( "3.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?<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 #762013 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the Normal distribution table of z-scores<BR>\n" );
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document.write( "1.  Probability(P) (X > 85) = 1 - P (X < 85)<BR>\n" );
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document.write( "z-score = (85 - 90)/5 = -1<BR>\n" );
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document.write( "P (X > 85) = 1 - 0.1587 = 0.8413<BR>\n" );
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document.write( "the probability that a randomly selected exam will have a score of at least 85 is 0.8413<BR>\n" );
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document.write( "2.  P (89 < X < 92) = P (X < 92) - P (X < 89)<BR>\n" );
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document.write( "z-score(92) = (92 - 90)/5 = 0.40<BR>\n" );
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document.write( "z-score(89) = (89 - 90)/5 = -0.20<BR>\n" );
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document.write( "P (89 < X < 92) = 0.6554 - 0.4207 = 0.2347<BR>\n" );
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document.write( "percentage with scores between 89 and 92 is 23.47 %<BR>\n" );
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document.write( "3.  1 - 0.025 = 0.975<BR>\n" );
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document.write( "0.975 is associated with z-score of 1.96<BR>\n" );
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document.write( "(X - 90)/5 = 1.96<BR>\n" );
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document.write( "X - 90 = 9.8<BR>\n" );
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document.write( "X = 99.8<BR>\n" );
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document.write( "the lowest score eligible for an award is 99.8<BR>\n" );
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