Suppose 30 control limits are constructed for the average temperature in a furnace. Samples of size 4 were selected with the average temperature being 5000 C and a standard deviation of 50 C, a. Find the 30 control charts. b. Suppose Rule 2 and Rule 3 are used simultaneously to determine out-of-control conditions. What is the overall probability of a Type I error assuming independence of the rules? c. Approximately how many samples, on average, will be analyzed before detecting a I change when Rules 2 and 3 are used simultaneously? d. If the process average drops to 4960, what is the probability of the shift being detected within the first two samples