Question

A student took two national aptitude tests. The mean 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. (Hint: See Example 3.18 )

Short answer

The student performed better on the test where the z-score is higher.

Step-by-step solution

Calculate Z-score for the first test.

Calculate the Z-score for the first test using the formula \( z = (X - μ) / σ \). In this case, X=625, μ=475 and σ=100. So, the Z-score for the first test would be \( z = (625 - 475) / 100 \).

Calculate Z-score for the second test.

Use the same formula to calculate the Z-score for the second test. Here, X=45, μ=30 and σ=8. So, the Z-score for the second test would be \( z = (45 - 30) / 8 \).

Compare Z-scores.

The test where the student's score has a higher z-score is the one the student performed better on, compared to others. Compare the calculated z-scores of the two tests.