document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191685>Question 1191685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The marks in English in a recent test had a mean of 76% with a standard deviation of 7%. The Science results had a mean of 84% with a standard deviation of 5%. Jasmine obtained scores of 86% in English and 89% in Science.\r<BR>\n" );
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document.write( "a) Which is the better result? Explain your answer.<BR>\n" );
document.write( "b) If there are 30 people in the class, estimate Jasmine's position in Science. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823483 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=823483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the marks in english have a mean of 76% with a standard deviation of 7%.<BR>\n" );
document.write( "the marks in science have a mean of 84% with a standard deviation of 5%.\r<BR>\n" );
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document.write( "jasmine obtained 86% in english and 89% in science.\r<BR>\n" );
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document.write( "use the z-score to compare these.\r<BR>\n" );
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document.write( "the z-score formula says 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, in this case.\r<BR>\n" );
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document.write( "for english, her z-score formula becomes z = (86 - 76) / 7 = 1.43, rounded to 2 decimal places.<BR>\n" );
document.write( "for science, her z-score formula becomes z = (89 - 84) / 5 = 1, no additional rounding required.\r<BR>\n" );
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document.write( "a z-score of 1.43 has a greater area under the normal distribution curve to the left of it.<BR>\n" );
document.write( "this indicates she scored higher, relative to her peers, in the english course.<BR>\n" );
document.write( "while she had a higher score in science, the rest of the class did better too, making her score less higher, relative to her peers.\r<BR>\n" );
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document.write( "fyi, a z-score of 1.43 has an area under the normal distribution curve equal to <BR>\n" );
document.write( ".92364 to the left of it and a z-score of 1 has an area under the normal distribution curve equal to .84134.\r<BR>\n" );
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document.write( "an area of .92364 to the left of the z-score means she was better than approximately 92% of her peers in english.<BR>\n" );
document.write( "an area of .84134 to the left of the z-score means she was better than approximately 84% of her peers in science.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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