Question

Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 90 clamps, the mean time to complete this step was 49.7 seconds. Assume that the population standard deviation is-7 seconds. Part 1 out of 2 Construct a 99% confidence interval for the mean time needed to complete this step. Round to one decimal place, if nec essary. A 99% confidence interval for the mean is

Answer 1

99% confidence interval for $\mu$ is

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

49.7 - 2.576 * 7 / sqrt(90) < $\mu$ < 49.7 + 2.576 * 7 / sqrt(90)

47.8 < $\mu$ < 51.6

The 99% CI for $\mu$ is ( 47.8 , 51.6)