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 75 clamps, the mean time to complete this step was 50.1 seconds. Assume that the population standard deviation is

σ = 10 seconds.

a. Construct a 95% confidence interval for the mean time needed to complete this step.

b. Find the sample size needed so that a 98% confidence interval will have margin of error of 1.5.