Answer to Question #332770 in Statistics and Probability for 8183K

Question

Many manufacturing problems involve the matching of machine parts, such as shafts fit into a

valve hole. A particular design requires a shaft with a diameter of 22.00mm, but shafts with

diameters between 21.99mm and 22.02mm are acceptable. Suppose that manufacturing

process yields shafts with diameters normally distributed, with a mean of 22.002mm and a

standard deviation of 0.005 mm. For this process,

a. What is the proportion of shafts with a diameter between 21.99 mm and 22.00 mm?

b. What is the probability that a shaft is acceptable?

c. Find what is diameter that will be exceeded by only 5 percent of the shafts?

d. What would be your answers in (a) through (c) if the standard deviation of the shaft

diameters were 0.004 mm?