Currently, professional men’s basketball players score an average of 18 point 2 points per game with a standard deviation of 4 point 5 points. The current top-scoring professional basketball player scores an average of 36 point 2 points per game. In one season in the 1990s, professional basketball players averaged 13 point 2 points per game with a standard deviation of 3 point 7 points. The top-scoring professional basketball player averaged 30 point 1 points per game. Which player did better relative to his peers?
Answer
A
The current basketball player did better than the 1990s basketball player because his z -score is higher.
B
The 1990s basketball player did better than the current basketball player because his z -score is closer to the mean.
C
The current basketball player did better than the 1990s basketball player because his z -score is closer to the mean.
D
The 1990s basketball player did better than the current basketball player because his z -score is higher.
Explanation
Compare each player’s score with the average in standard-deviation units: the current player’s z-score is (36.2 − 18.2) ÷ 4.5 = 4. The 1990s player’s z-score is (30.1 − 13.2) ÷ 3.7 ≈ 4.57, which is higher, so the 1990s player scored farther above his peers’ average.
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