Question

Lecture18: Problem 7 Previous Problem List Next (1 point) The diameter of the twelve-penny common nails made by 'Snails!, Inc., is normally distributed with standard deviation 0.004 in. A sample of 37 such nails was found to have a mean diameter of 0.127 in. Find a 90% confidence interval for the mean diameter of all such nails. Round the endpoints to five decimal places. Confidence interval is ( Note: You can earn partial credit on this problem. Note: You can get a new version of this problem after the due date. Preview My Answers Submit Answers

Answer 1

90% confidence interval for $\mu$ is

$\bar{x}$ - Z$\alpha$/2 * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x}$ + Z$\alpha$/2 * $\sigma$ / sqrt(n)

0.127 - 1.645 * 0.004 / sqrt(37) < $\mu$ < 0.127 + 1.645 * 0.004 / sqrt(37)

0.12592 < $\mu$ < 0.12808

Confidence interval is (0.12592 , 0.12808 )