Question

Employees in a large manufacturing plant worked an average of 62 hours of overtime last year, with a standard deviation of 15 hours. The union president and the human resources director jointly selected a sample of 36 employees and had discussions on the company’s work rules and overtime policies. What is the probability that employees in this sample worked an average of less than 65 hours of overtime?

Answer 1

$\mu=62 \\ \sigma = 15 \\ n=36 \\ P(\bar{x}<65) = P(Z< \frac{65-62}{15 / \sqrt{36}}) \\ = P(Z< 1.2) \\ = 0.8849\; (from \;standard\; normal\; table)$