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?

Answer 1

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%