In a statistically based quality improvement project for the turning of steel shafts it was observed that about 23 percent of the shafts failed to meet specifications. Those failures were divided into reworkable shafts and scrap. The overall scrap rate was 3 percent of total production. (a) Suppose that p = 0.2 is indeed a sensible figure for the chance that a given shaft will be reworkable. Suppose further that n = 10 shafts will be inspected, and that the probability that at least two are classified as reworkable is to be evaluated for process compliance monitoring. Find that probability. (b) In a production situation an investigator found this pattern of results: 40 shafts in specification, then 10 reworkable shafts, then a tool change, then 40 shafts in specification, and so on. Is the probability computed in (a) reasonable?