A process for making steel pipe is under control if the diameter of the pipe has mean 3.0 in. with standard deviation of no more than 0.0250 in. To check whether the process is under control, a random sample of size n = 30 is taken each day and the null hypothesis μ = 3.0 is rejected if X-bar is less than 2.9960 or greater than 3.0040. Find
(a) The probability of type I error;
(b) The probability of type II error when μ = 3.0050 in. Assume σ = 0.0250 in.