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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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  1. 30 April, 15:02
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    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.
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