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.The top 2.5 percent of the applicants would have a score of at least (choose the nearest integer):
A) 606.
B) 617.
C) 600.
D) 646

Question

Quizplus · Accepted Answer

We need to find the score that corresponds to the top 2.5% of the distribution. We can use the z-score formula for this:

z = (x - mu) / sigma

Where:
x = the score we're looking for
mu = the mean (460)
sigma = the standard deviation (80)

To find the z-score corresponding to the top 2.5%, we look up the z-score from the standard normal distribution table:

z = 1.96

Now we can plug in the values and solve for x:

1.96 = (x - 460) / 80

x - 460 = 1.96 * 80

x = 617.6

Rounding to nearest integer: 618. Therefore, the answer is B.

A Large Number of Applicants for Admission to Graduate Study