2. (20 points) A manufacturer wishes to maintain a process average of 1% nonconforming product or less. It is decided to sample 250 units each day to control production. (a) (5 points) Find the 3-sigma control limits of a p chart for this process. (b) (5 points) Find the 3-sigma control limits of a np chart for this process. (c) (5 points) Suppose that the process shifts from 1% to 4% nonconforming product. Find the probability that the shift will be detected by the np chart on the first day after the shift occurs. (use Normal approximation) (d) (5 points) If we want the probability of detecting (by p chart) the shift described in (c) to be at least 0.5, what should the sample size be?