A university wants to select individuals for their honors program partly on the basis of SAT scores. Total scores for the three parts of the test are approximately normally distributed with mean 1500 and standard deviation 250. If they want only the top 5% to qualify, they use the corresponding z-score of 1.645 within the formula X

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Kadyn Bowen

2 August, 09:48

A university wants to select individuals for their honors program partly on the basis of SAT scores. Total scores for the three parts of the test are approximately normally distributed with mean 1500 and standard deviation 250. If they want only the top 5% to qualify, they use the corresponding z-score of 1.645 within the formula X

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1920

Explanation:

Since you are using the z-score with 95% of area under the curve to its left, to get only the top students, you need to multiply (1.645 x standard deviation) + mean to determine the minimum SAT score.

minimum SAT score to fall under the top 95% = (1.645 x 250) + 1,500 = 411.25 + 1500 = 1911.25 ≈ 1920 (round up)