A student took a chemistry exam where the exam scores were mound-shaped with a mean score of 90 and a standard deviation of 64. She also took a statistics exam where the scores were mound-shaped, the mean score was 70 and the standard deviation was 16. If the student's grades were 102 on the chemistry exam and 77 on the statistics exam, then:
A) the student did relatively better on the chemistry exam than on the statistics exam, compared to the other students in each class.
B) the student did relatively better on the statistics exam than on the chemistry exam, compared to the other students in the two classes.
C) the student's scores on both exams are comparable, when accounting for the scores of the other students in the two classes.
D) it is impossible to say which of the student's exam scores indicates the better performance.
E) the student did relatively the same on both exams.

Question

Quizplus · Accepted Answer

We can compare the student's performance on each exam by converting their scores into z-scores, which tell us the number of standard deviations above or below the mean a score is. Using the formula z = (score - mean) / standard deviation, we get:
z_chemistry = (102 - 90) / 64 = 0.1875
z_statistics = (77 - 70) / 16 = 0.4375
The positive z-scores indicate that the student scored above the mean for each class, but the z-score for the statistics exam is larger than the z-score for the chemistry exam. This means that the student did relatively better on the statistics exam than on the chemistry exam compared to the other students in the two classes. Choice B is the correct answer.

A Student Took a Chemistry Exam Where the Exam Scores