Problem 2 (20 pts) A three-sigma fraction nonconforming control chart with center line 0.15, UCL = 0.27, and LCL = 0.03 is used to control a process. The sub-sample size for all samples is the same (fixed subsample size). (a) (5pts) Find the sub-sample size for the used p-chart (round the number). (b) (5pts) Find the probability of type I error (Use the Poisson approximation). 5 (c) (5pts) Find the probability of type II error if the process fraction defective is actually p = 0.25 (Use the Poisson approximation). (d) (5pts) Find ARL0 and ARL1 for p = 0.25