The graduating class obtained mu = 75 and sigma = 5 in English and mu = 78 and s

Question

The graduating class obtained mu = 75 and sigma = 5 in English and mu = 78 and sigma = 4 in History. Find the z-score of a score (X) that is (a.1) 5 points above and another that is (a.2) 6 points below the English mu; (a.3) 7 points above and (.4) 8 points below the History mu. Determine the raw scores corresponding to the following z-scores in History: b.1) z = -1.65 (b.2) z = 1.96. You obtained a raw score of 90 in both English and History. Compared to the entire class, in which course did you do better? Briefly explain your answer. Assume that both the English and the History tests were transformed into a standardized distribution with mu = 100 and sigma = 15. I f Paul's raw score of 80 in both original tests are standardized, in which course did he do better? Briefly explain your answer.

Explanation / Answer

a)

Note that z = (x-u)/sigma.

a.1

Hence, as x - u = 5, sigma = 5,

z = 5/5 = 1 [ANSWER]

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a.2

As x - u = -6, sigma = 5, then

z = -6/5 = -1.2 [ANSWER]

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a.3

As x - u = 7, sigma = 4,

z = 7/4 = 1.75 [ANSWER]

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a.4

As x - u = -8,

z = -8/4 = -2 [ANSWER]

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