A particular manufacturing design requires a shaft with a diameter of 19.000 mm, but shafts with diameters between 18.991 mm and 19.009 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 19.003 mm and a standard deviation of 0.006 mm. Complete parts (a) through (d) below.

a. for this process, what is the proportion of shafts with a diameter between 18.991 mm and 19.009 mm?

the proportion of shafts with diameter of 18.991 mm and 19.000 mm is

b. For this process what is the probability that a shaft isacceptable?

c. For this process what is the diameter that will be exceeded by only 1% of theshafts?

d. What would be your answers to parts(a) through(c) if the standard deviation of the shaft diameters were is 0.005 mm?