A process is controlled with a fraction nonconforming control chart with three-sigma limits, = 100, center line = 0.078.

(a) Find the upper and lower control limit for the fraction nonconforming chart

(b) Find the equivalent control chart for the number nonconforming.

(c) 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?