A large manufacturing firm tests job applicants who recently graduated from college. The test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution. What is the lowest score a college graduate must earn to qualify for a responsible position?
A) 50
B) 625
C) 460
D) 578

Question

Quizplus · Accepted Answer

To find the score that falls in the upper 6 percent of the distribution, we need to find the z-score associated with that percentage.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the upper 6 percent is approximately 1.64.

We can then use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score we're looking for, μ is the mean, and σ is the standard deviation.

Plugging in the values we know, we get:

1.64 = (x - 500) / 50

Solving for x, we get:

x = 1.64 * 50 + 500 = 578

Therefore, the lowest score a college graduate must earn to qualify for a responsible position is 578.

A Large Manufacturing Firm Tests Job Applicants Who Recently Graduated