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 dollars. What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000?
A) 0.5889
B) 0.7486
C) 0.8413
D) 0.9048

Question

Quizplus · Accepted Answer

The probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000 is 0.5889. This can be calculated using the normal distribution with mean µ = $54,000 and standard deviation σ = $12,000. The z-score for $50,000 is (50,000 - 54,000) / 12,000 = -0.3333, and the z-score for $60,000 is (60,000 - 54,000) / 12,000 = 0.5. The probability that the average salary is between these two z-scores is the area under the normal distribution curve between -0.3333 and 0.5, which is 0.5889.

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