A statistical process control chart example. Samples of 18 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 18 that require rework. A process problem is suspected if X exceeds its mean by more than three standard deviations.

If the percentage of parts that require rework remains at 1%, what is the probability that X exceeds its mean by more than three standard deviations?