Question
For one test's distribution (mu = 447, sigma = 94) and another test's distribution (mu = 22, sigma = 5) which score is relatively higher, a score of 685 on the first test or a score of 30 on the second test? Explain. Select the most appropriate answer from those below. A. The first score is relatively higher than the second score because the z-score on the first test is equal to the z-score of the score on the second test. B. The second score is relatively higher than the first score because the z-score of the score on the first test is less than the z-score of the score on the second test. C. The test scores are equally high because the z-score of the score on the first test is equal to the z-score on the second test. D. The first score is relatively higher than the second score because the z-score of the score on the first test is greater than the z-score of the score on the second test.
Explanation / Answer
z-score corresponding to a score of 685 in first case = (685 - 447) / 94 = 2.5319.
z-score corresponding to a score of 30 in the second case = (30 - 22) / 5 = 1.6.
So, the first score is relatively higher, since its' z-score is higher than the second score. Hence Option(D) is the correct choice. (Ans).
