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?
A)0.2734
B)0.7734
C)0.7266
D)0.7500

Question

Quizplus · Accepted Answer

To find the fraction of applicants with a score of 400 or above, we calculate the Z-score for 400 using the formula Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. For a score of 400, Z = (400 - 460) / 80 = -60 / 80 = -0.75. Looking up the Z-score of -0.75 in a standard normal distribution table or using a calculator, we find that the area to the right (which represents the fraction of applicants scoring 400 or above) is approximately 0.7734.

A Large Number of Applicants for Admission to Graduate Study