Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?
A) 0.1587
B) 0.3085
C) 0.6915
D) 0.8413

Question

Quizplus · Accepted Answer

The standard error of the mean for four electricians is σ/√n = $12,000/2 = $6,000. The z-score for $60,000 is (60,000 - 54,000) / 6,000 = 1. The probability that the average salary exceeds $60,000 corresponds to the area to the right of z = 1, which is 1 - 0.8413 = 0.1587.

Suppose That, on Average, Electricians Earn Approximately µ = $54,000