Suppose we examine the distribution of scores on the last exam separately for fr
ID: 2948392 • Letter: S
Question
Suppose we examine the distribution of scores on the last exam separately for freshman and sophomores. Both distributions are approximately normally distributed and have the same mean, but the distribution of exam scores had a smaller standard deviation among sophomores than freshman. A z-score is calculated for Mary’s exam score relative to both distributions (freshman and sophomores). Given that Mary’s score is well above the mean, which of the following would be true about these two z-scores?
a. The z-score based on the distribution for the freshman students would be higher.
b. The z-score based on the distribution for the sophomore students would be higher.
c. The two z-scores would be the same.
d. There is not enough information to determine
Explanation / Answer
Since the z - score is inversely proportion to the standard deviation, z-score based on the distribution for the sophomore students would be higher.
Option B is correct.