Many manufacturing problems involve the accurate matching of machine parts, such as shafts, that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm, but shafts with diameters between21.900 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields shafts that are normally distributed with a mean of 22.002 mm and a standard deviation of 0.005 mm. For this process, what is:
(a) the proportion of shafts with a diameter between 21.900 mm and 22.000 mm?
(b) the probability that a shaft is acceptable?
(c) the diameter that will be exceeded by only 2% of the shafts?