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 of100clamps, the meantime to work this step was45.2seconds. Assume that the population standard deviation is=7 seconds. Round the critical value to no less than three decimal places.

(a) Construct a99.9%confidence interval for the meantime needed to finish this step. Round the answer to at least one decimal place.