On this semester’s final exam, Susie scored 72 on her classics exam (class distribution: μ =
65, σ = 3.57) and 53 on her psychology exam (class distribution: μ = 49, σ = 2.04). For
which exam should Susie expect the better grade?
a. Classics
b. Psychology
c. The two exam scores are equivalent.
d. Cannot answer without additional information.
You should standardize her test scores, which means find the z-score of each and compare the two.
Z = (score-mean)/SD
Compare the two Z scores.
Psychology
To determine for which exam Susie should expect the better grade, we need to compare her scores relative to the class distributions using z-scores.
The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the individual score, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Let's calculate the z-scores for each exam:
For the classics exam:
z_classics = (72 - 65) / 3.57 = 1.96
For the psychology exam:
z_psychology = (53 - 49) / 2.04 = 1.96
Both z-scores are the same, which means Susie's score on both exams is the same relative to their respective class distributions. Therefore, the correct answer is:
c. The two exam scores are equivalent.