A high school student took two college entrance exams and scored 1120 on the sat and 27 on the act. suppose that sat scores have a mean of 950 and a standard deviation of 140 while the act scores have a mean of 22 and a standard deviation of 4. assuming that the performance on both tests follows a normal distribution, determine which test the student did better on.

Question

Jarvis

Mathematics

30 April, 14:47

A high school student took two college entrance exams and scored 1120 on the sat and 27 on the act. suppose that sat scores have a mean of 950 and a standard deviation of 140 while the act scores have a mean of 22 and a standard deviation of 4. assuming that the performance on both tests follows a normal distribution, determine which test the student did better on.

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Answers (1)

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Aaliyah Vance · Answer 1

We can compare performance by comparing z-scores. The higher z-score indicates better performance relative to others taking the same test. The z-score of a particular test score (x) is ...

... z = (x - μ) / σ

SAT

z = (1120 - 950) / 140 ≈ 1.21

ACT

z = (27 - 22) / 4 ≈ 1.25

Summary

Relative to other students taking these tests, the student did better on the ACT.