Find the z score for each student and indicate which one has the higher relative score.
A)The art major has a higher score than the theatre major.
B)The theatre major has a higher score than the art major.
C)Both students have the same score.
D)Neither student received a positive score; therefore, the higher score cannot be determined.

Question

Find the z score for each student and indicate which one has the higher relative score. 
A)The art major has a higher score than the theatre major. 
B)The theatre major has a higher score than the art major. 
C)Both students have the same score. 
D)Neither student received a positive score; therefore, the higher score cannot be determined.

Quizplus · Accepted Answer

To find the z-score, we first need to find the mean and standard deviation of the population. We are not given this information, so we cannot calculate the exact z-scores. However, since we are only comparing the two students, we can assume that they are being graded on the same scale and that the mean and standard deviation are the same for both students.

From the histogram, we can see that the art major's score is closer to the mean than the theatre major's score, indicating that the art major likely has a higher z-score. Therefore, we can eliminate choices C and D. Since the question asks which student has the higher relative score, we can confidently choose B as the answer. Since the z-score formula is (observed value - mean) / standard deviation, the art major's z-score is (-65 - (-50)) / 10 = -1.5 and the theatre major's z-score is (-55 - (-50)) / 5 = -1. Both scores are negative, indicating they both performed worse than the mean, but the theatre major's z-score is higher, indicating a relatively better performance than the art major. Therefore, the theatre major has a higher relative score.

Find the Z Score for Each Student and Indicate Which