Suppose bolts are being manufactured using a process so that it is known that the length of the bolts follows a normal distribution with standard deviation 50 mm. The manufacturer wants to check that the mean length of their bolts is 160 mm, and so takes a sample of 50 bolts and uses a one tail test with ? = .01 (i.e. H0: µ ? 160). What is the probability of a type II error if the actual mean length is 162.5?. Draw the power curve.