document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171133>Question 1171133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student scores 60 on a Mathematics test that has a mean of 54 and a standard deviation of 3, and she scores 80 on a history test with a mean of 75 and a standard deviation of 2. On which test did she perform better?<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 #796038 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the z-score formula to determine the answer to this.<BR>\n" );
document.write( "z-score formula is:<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "math test has mean of 54 with standard deviation of 3.<BR>\n" );
document.write( "z = (60 - 54) / 3 = 6/3 = 2.<BR>\n" );
document.write( "area to the left of that z-score = .977249938.<BR>\n" );
document.write( "round to 3 decimal places to get .977<BR>\n" );
document.write( "multiply by 100 to get z-score of 2 is greater than 97.7% of all possible z-scores.\r<BR>\n" );
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document.write( "history test has mean of 75 with standard deviation of 2.<BR>\n" );
document.write( "z = (80 - 75) / 2 = 5/2 = 2.5<BR>\n" );
document.write( "area to the left of that z-score = .9937903201.<BR>\n" );
document.write( "round to 3 decimal places to get .994<BR>\n" );
document.write( "multiply by 100 to get z-score of 2.5 is greater than 99.4% of all possible z-scores.\r<BR>\n" );
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document.write( "she performed better on the history exam.\r<BR>\n" );
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document.write( "i used the t-84 plus to find the probabilities.<BR>\n" );
document.write( "if you used the z-score table, you would do the following.<BR>\n" );
document.write( "look up the z-score (rounded to 2 decimal places) in the table to find the area under the normal distribution curve to the left of that z-score.\r<BR>\n" );
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document.write( "with a z-score of 2.00, the area to the left of the z-score is shown as .97725 = .977 rounded to 3 decimal places * 100 = 97.7%.<BR>\n" );
document.write( "with a z-score of 2.50, the area to the left of the z-score is shown as .99379 = .994 rounded to 3 decimal places * 100 = 99.4%.\r<BR>\n" );
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document.write( "the table i used can be found at <a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
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