Question

Chris is enrolled in a college algebra course and earned a score of 260 on a math placement test that was given on the first day of class. The instructor looked at two distributions of scores – one is the distribution for all first year college students who took the test, and the other is a distribution for students enrolled in this algebra class. Both are approximately normal and have the same mean, but the distribution for the algebra class has a smaller standard deviation. A z-score is calculated for Chris’ test score in both distributions (all first year college students and all algebra class students). Given that Chris’ 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 algebra students would be higher.

b) The z-score based on the distribution for all first year college students would be higher.

c) The two z-scores would be the same.

d) There’s not enough information to answer this question.

Answer 1

It is given that there are two groups: one is all first year college students and all algebra class students.

Both the groups are approximately normal and have the same mean, but the distribution for the algebra class has a smaller standard deviation.

A z-score is calculated for Chris’ test score in both distributions (all first year college students and all algebra class students).

Also Chris’ score is well above the mean.

The z-score formula is,

Where x represents raw score, represents mean and represents standard deviation.

From the above formula, it is clear that if the standard deviation is larger than the z-score is smaller and if the standard deviation is smaller than the z-score is larger.

From the given information, it is clearly mentioned that the distribution for the algebra class has a smaller standard deviation. Therefore, it can be said that the z-score based on the distribution for the algebra students would be higher.

Hence, the correct option is a).