Kane measures the concentricity as a positive deviation using a dial indicator gauge. Historically, this process has produced an average concentricity of 5.6 with a standard deviation of 0.7. To monitor this process, he periodically takes a random sample of three measurements. If the average is greater than 6.8 or less than 4.3, he concludes that the process mean has shifted. Assume that the process mean is 5.6.
a) Find the probability that on the next sample he concludes the process mean has shifted purely due to random chance.
b) What did you assume in order to find this probability?