A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a process . 1. If three-sigma limits are used, find the sample size for the control chart. 2. Use the Poisson approximation to the binomial to find the probability of type I error. 3. Use the Poisson approximation to the binomial to find the probability of type II error if the process fraction defective is actually p = 0.20. 4. Find the average run length to detect a shift to a fraction non-conforming of 0.15.