5-A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ =0.001 millimeters. A random sample of 15 rings has a mean diameter of x = 74.036 millimeters. (a) Construct a 99% two-sided confidence interval on the mean piston ring diameter. (b) Construct a 95% lower-confidence bound on the mean piston ring diameter.