document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200310>Question 1200310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dwayne and Lloyd began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Dwayne took a test in Science and earned a 78.6, and Lloyd took a test in Math and earned a 65.5. Use the fact that all the students' test grades in the Science class had a mean of 73.5 and a standard deviation of 10.4, and all the students' test grades in Math had a mean of 62.8 and a standard deviation of 11.1 to answer the following questions.\r<BR>\n" );
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document.write( "Calculate the z-score for Dwayne's test grade.\r<BR>\n" );
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document.write( "Calculate the z-score for Lloyd's test grade. </SPAN>\n" );
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document.write( "The z-score formula is<BR>\n" );
document.write( "z = (x - mu)/sigma\r<BR>\n" );
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document.write( "In the numerator we're computing how far the score x is from the mean (mu)<BR>\n" );
document.write( "The numerator is negative if x is below mu. This leads to a negative z-score.<BR>\n" );
document.write( "The numerator is positive if x is above mu. This leads to a positive z-score.\r<BR>\n" );
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document.write( "Dividing that result over sigma tells us how far we are from the mean in terms of standard deviation (sigma) units. <BR>\n" );
document.write( "Doing this computation standardizes each test score to allow for comparison.\r<BR>\n" );
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document.write( "Let's calculate the z-score for Dwayne.<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (78.6-73.5)/10.4<BR>\n" );
document.write( "z = 0.49038461538461<BR>\n" );
document.write( "z = 0.49\r<BR>\n" );
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document.write( "Do the same for Lloyd.<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (65.6 - 62.8)/11.1<BR>\n" );
document.write( "z = 0.25225225225226<BR>\n" );
document.write( "z = 0.25\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Dwayne: z = 0.49<BR>\n" );
document.write( "Lloyd: z = 0.25\r<BR>\n" );
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document.write( "Therefore, Dwayne performed better on his test compared to Lloyd, since Dwayne has the higher z-score. <BR>\n" );
document.write( "He is further to the right on the normal distribution scale. <BR>\n" );
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