A student took two national aptitude tests. The mean and standard deviation were 675 and 100,
respectively, for the first test, and 50 and 10, respectively, for the second test. The student scored 825 on
the first test and 70 on the second test. Use z-scores to determine on which exam the student performed
better relative to the other test takers.
first exam
second exam
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To determine on which exam the student performed better relative to the other test takers, we need to compare their scores in terms of z-scores.
First, we calculate the z-score for the first test:
z = (x - mean) / standard deviation
z1 = (825 - 675) / 100
z1 = 1.5
Next, we calculate the z-score for the second test:
z2 = (70 - 50) / 10
z2 = 2
A higher z-score indicates a better performance relative to other test takers. Therefore, the student performed better on the second exam relative to the other test takers, as their z-score of 2 is higher than the z-score of 1.5 on the first exam.
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