Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother’s score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire’s mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance?
Answer
A
Claire did better because her z-score is greater than her mother’s.
B
Claire’s mother did better because her z-score is greater than Claire’s.
C
Claire did better because her z-score is closer to the mean than her mother’s.
D
Claire’s mother did better because her z-score is closer to the mean than Claire’s.
Explanation
Compare each score with the mean for the year she took the exam using z = (score − mean) ÷ standard deviation. Claire’s z-score is (690 − 510) ÷ 110 ≈ 1.64, while her mother’s is (680 − 490) ÷ 100 = 1.90. Since her mother’s score was more standard deviations above her year’s mean, Claire’s mother had the better relative performance.
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