(Solved): A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is no ...

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with \( \sigma=0.001 \) millimeters. A random sample of 15 rings has a mean diameter of \( \bar{x}=74.036 \) millimeters. (a) Construct a \( 99 \% \) two-sided confidence interval on the mean piston ring diameter. (b) Construct a \( 99 \% \) lower confidence bound on the mean piston ring diameter. (c) Compare the lower bound in part (b) with the confidence interval in part (a).