Assume that the national SAT score has a mean of 1000 and st

Assume that the national SAT score has a mean of 1000 and standard deviation of 200 and the national ACT score has a mean of 27 and standard deviation of 3. Suppose a student took both tests and scored 1260 in SAT and scored 33 in ACT. You must show work to get credit.

a. What are the relative z-scores?

b. In which test did the student scored higher based on the z-score?

Solution

a)

For the one who took SAT:

z = (x-u)/sigma = (1260-1000)/200 = 1.3 [ANSWER]

For the one who took ACT:

z = (x-u)/sigma = (33-27)/3 = 2 [ANSWER]

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b)

The one who took ACT has a relative higher score. [ANSWER, ACT]