Past experience of a large manufacturing firm with administering a test to recent college graduates who had applied for a job revealed that the mean test score was 500, and the standard deviation was 50. The distribution of the test scores was normal. Based on this experience, management is considering placing a person whose score is in the upper 6 percent of the distribution directly into a responsible position. 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

First, we need to find the z-score corresponding to the upper 6 percent of the distribution. Using a standard normal distribution table, we find that the z-score corresponding to the upper 6 percent is approximately 1.56.

z = (X - μ) / σ

1.56 = (X - 500) / 50

Solving for X, we get:

X = 500 + 1.56(50)

X = 578

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

Option A (50) is incorrect because it is the value of the standard deviation, not the score needed to qualify for a responsible position.

Option B (625) is incorrect because it is not the score corresponding to the upper 6 percent of the distribution.

Option C (460) is incorrect because it is below the mean and not the score corresponding to the upper 6 percent of the distribution.

Past Experience of a Large Manufacturing Firm with Administering a Test