The graduating class obtained µ= 75 and ?= 5 in English and µ= 78 and ?= 4 in Hi

Question

The graduating class obtained µ= 75 and ?= 5 in English and µ= 78 and ?= 4 in History. a. 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 µ; (a.3) 7 points above and (a.4) 8 points below the History µ. (4 pts) b. Determine the raw scores corresponding to the following z-scores in History: (b.1) z = -1.65 (b.2) z = 1.96. (4 pts) c. 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. (5 pts) d. Assume that both the English and the History tests were transformed into a standardized distribution with µ= 100 and ?= 15. If Paul’s raw score of 80 in both original tests are standardized, in which course did he do better? Show his new scores after being transformed into the standardized distribution. Briefly explain your answer.

Explanation / Answer

Ans:

a-1)

z=5/5=1

a-2)

z=-6/5=-1.2

a-3)

z=7/4=1.75

a-4)

z=-8/4=-2

b)

b-1)

x=78-1.65*4=71.4

b-2)

x=78+1.96*4=85.84

c)

z score for English:

z=(90-75)/5=3

z score for History:

z=(90-78)/4=3

As,z score is same in both subjects,so performance is equal.

d)

For English,zold=(80-75)/5=1

For History,zold=(80-78)4=0.5

new score for english:

zold=znew

x=100+1*15=115

new score for history:

x=100+0.5*15=107.5

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