A process is controlled with a fraction nonconforming control chart with three-sigma limits, n = 100, UCL = 0.161, center line = 0.080, and LCL = 0.

a. Find the equivalent control chart for the number nonconforming.
b. Use the Poisson approximation to the binomial to find the probability of a type I error.
c. Use the normal approximation to binomial to find the probability of a type II error if the process fraction nonconforming shifts to 0.2.
d. What is the probability of detecting the shift in part (c) by at most the fourth sample after the shift?