document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197495>Question 1197495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two standardized​ tests, test A and test​ B, use very different scales. Assume that in one year the distribution of scores on test A can be modeled by N(1100,25)and scores on test B can be modeled by N(11,2) . If an applicant to a university has taken test A and scored 1190 and another student has taken test B and scored 15 ​, compare these​ students' scores using​ z-values. Which one has a higher relative​ score? Explain.<BR>\n" );
document.write( "The​ z-value of the test A score is <BR>\n" );
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document.write( "enter your response here.<BR>\n" );
document.write( "​(Round to two decimal places as​ needed.) <BR>\n" );
document.write( "Part 2<BR>\n" );
document.write( "The​ z-value of the test B score is <BR>\n" );
document.write( "  <BR>\n" );
document.write( "enter your response here.<BR>\n" );
document.write( "​(Round to two decimal places as​ needed.)  </SPAN>\n" );
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document.write( "Test A's scores are distributed according to N(1100,25)<BR>\n" );
document.write( "We have a normal distribution with mean mu = 1100 and standard deviation sigma = 25<BR>\n" );
document.write( "The template is N(mu, sigma)\r<BR>\n" );
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document.write( "If a person gets a score of x = 1190 on test A, then,<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (1190 - 1100)/25<BR>\n" );
document.write( "z = 3.6<BR>\n" );
document.write( "This person got a score exactly 3.6 standard deviations above the mean.\r<BR>\n" );
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document.write( "Test B's scores are distributed by N(11,2)<BR>\n" );
document.write( "mu = 11<BR>\n" );
document.write( "sigma = 2<BR>\n" );
document.write( "If a person scored x = 15 on this test, then,<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (15 - 11)/2<BR>\n" );
document.write( "z = 2<BR>\n" );
document.write( "This person got a score 2 standard deviations above the mean.\r<BR>\n" );
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document.write( "We see that the person taking test A did better compared to their peers. By \"peers\" I mean the people taking the same test. \r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "z score for test A: <font color=red>3.6</font><BR>\n" );
document.write( "z score for test B: <font color=red>2</font><BR>\n" );
document.write( "Who has a higher relative score? The person who took <font color=red>test A</font><BR>\n" );
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