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Answer :
The answer explains how to calculate z-scores for SAT scores, interpret them, and compare scores between SAT and ACT tests.
Z-score Calculation:
a. For an SAT score of 720, the z-score is calculated as (720-520)/115 = 1.74. This indicates that a score of 720 is 1.74 standard deviations above the mean.
b. A math SAT score 1.5 standard deviations above the mean of 520 is 520 + 1.5(115) = 692.5.
c. To determine who did better, we calculate the z-scores for the SAT score of 700 and the ACT score of 30. The z-score for the SAT score of 700 is (700-514)/117 ≈ 1.59, while the z-score for the ACT score of 30 is (30-21)/5.3 ≈ 1.70. Comparing these values, the person with the ACT score of 30 performed slightly better.
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