A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a

Question

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of the applicants would you expect to have a score of 400 or above?

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Kaylee 2 weeks 2021-10-10T22:00:55+00:00 1 Answer 0

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    2021-10-10T22:02:17+00:00

    Answer:

    The fraction or percentage of the applicants that we would expect to have a score of 400 or above is 77.34%

    Step-by-step explanation:

    Scores are normally distributed with a mean of 460 and a standard deviation of 80. For a value x, the associated z-score is computed as z = \frac{x-460}{80}, therefore, the z-score for 400 is given by z_{0} = (400-460)/80 = -0.75. To compute the fraction of the applicants that we would expect to have a score of 400 or above, we should compute the probability P(Z > -0.75) = 0.7734, i.e., the fraction or percentage of the applicants that we would expect to have a score of 400 or above is 77.34%

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