Answer to Question #271522 in Statistics and Probability for nesri

Question

Suppose the mean length of time between submission of a state tax return requesting a refund and the issuance of the refund is 47 days, with standard deviation 6 days. Find the probability that in a sample 50 of returns requesting a refund, the mean such time will be more than 50 days

Answer 1

$\mu = 47 \\ \sigma = 6 \\ n=50 \\ P(\bar{X} > 50) = 1 -P(\bar{X} < 50) \\ = 1 -P(Z< \frac{50-47}{6 / \sqrt{50}}) \\ = 1 -P(Z< \frac{3}{0.848}) \\ = 1 -P(Z< 3.537) \\ = 1 -0.99979 \\ = 0.00021$