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 21.990 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

1. The proportion of shafts with a diameter between 21.99 mm and 22.00 mm?

2. The probability that a shaft is acceptable?

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

4. What would be your answers in (1) through (3) if the standard deviation of the shaft diameters were 0.004 mm?