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Chapter 4: Problem 41

A student took two national aptitude tests. The national average and standard deviation were 475 and 100 , respectively, for the first test and 30 and 8 , respectively, for the second test. The student scored 625 on the first test and 45 on the second test. Use \(z\) scores to determine on which exam the student performed better relative to the other test takers.

Short Answer

Expert verified
The student performed better on the second test, relative to other test takers.

Step by step solution

01

Calculate z-score for the first test

To calculate the z-score, you subtract the mean from an individual raw score and then divide the difference by the standard deviation. So, for the first test, the z-score can be calculated as follows: \(z_1 = \frac{{625 - 475}}{{100}} = 1.5\)
02

Calculate z-score for the second test

Following the same method, for the second test, the z-score can be calculated as follows: \(z_2 = \frac{{45 - 30}}{{8}} = 1.875\)
03

Compare z-scores

Now that both z-scores are calculated, they can be compared. A higher z-score indicates a better performance relative to other test takers. Hence, since the z-score for the second test (1.875) is higher than the z-score for the first test (1.5), it can be concluded that the student performed better on the second test, relative to the other test takers.

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