A pacemaker is made up of several biomedical components that must be of a high quality for the pacemaker to work. It is vitally important for manufacturers of pacemakers to use parts that meet specifications. One particular plastic part, called a connector module, mounts on the top of the pacemaker. Connector modules are required to have a length between .304 inch and .322 inch to work properly. Any modules with length outside these limits are “out-of-spec.” Quality (Aug. 1989) reported on one supplier of connector modules that had been shipping out-of-spec parts to the manufacturer for 12 months.

a. The lengths of the connector modules produced by the supplier were found to follow an approximate normal distribution with mean μ = .3015 inch and standard deviation σ = .0016 inch. Use this information to find the probability that the supplier produces an "out-of-spec" part.

b. Once the problem was detected, the supplier’s inspection crew began to employ an automated data-collection system designed to improve product quality. After 2 months, the process was producing connector modules with mean μ = .3146 inch and standard deviation σ = .0030 inch. Find the probability that an "out-of-spec" part will be produced. Compare your answer to part a.