Question: Many manufacturing problems involve the 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 between 21.900 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields shafts with diameters 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 21.90 mm and 22.00 mm?

b. the probability that a shaft is acceptable?

c. the diameter that will be exceeded by only 2% of the shafts?

d. What would be your answers in (a) through (c) if the standard deviation of the shaft diameters was 0.004 mm?