Question

Mary and Jane both took PSY230 last semester but were in different sections taught by different professors. Mary's class had a mean grade of 85 points with a standard deviation of 5 points, while Jane's class had a mean grade of 80 points with a standard deviation of 10 points. Both Mary and Jane earned 88 points. Who did better in the class?

a) Mary did better.
b) Jane did better.
c) Mary and Jane did equally well.
d) It is impossible to tell.

Answer 1

By calculating the z-scores for Mary (0.6) and Jane (0.8), we can conclude that Jane did better in her class as her score is further above the mean compared to Mary.

Step-by-step explanation:

The question asks us to determine whether Mary or Jane did better in their PSY230 class given their scores, the mean scores, and the standard deviations of their respective classes. To address this, we need to calculate the z-scores for Mary and Jane's grades. The z-score is a measure of how many standard deviations an element is from the mean.

For Mary, the z-score is calculated as (X - M) / SD, where X is Mary's score, M is the mean score for Mary's class, and SD is the standard deviation for Mary's class. Plugging Mary's values in gives us the following calculation:

ZMary = (88 - 85) / 5 = 0.6

For Jane, we follow the same formula:

ZJane = (88 - 80) / 10 = 0.8

Since Jane's z-score is higher, this indicates that Jane's score is further above her class mean than Mary's is above her class mean. Therefore, Jane did better relative to her own class performance than Mary did.