Thank you very much. Problem 3: Find the answers for the following problems: 1) What is the type I error for x-bar control charts with

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Problem 3: Find the answers for the following problems: 1) What is the type I error for x-bar control charts with k = 3.11, and sample size of n=4? 2) Assume the mean shift is 1.50 (o is the process standard deviation), what is the type II error for detecting this mean shift using this control chart? 3) What is the probability that the out-of-control condition will be detected on the moh sample following the mean shift? 4) What is the expected number of subgroups analyzed until the mean shift is detected? 5) What is the probability that the first two samples following the mean shift produces a statistic that plots inside the control limits? 6) What is the probability that three consecutive samples produce statistics that plot outside of the control limits following the shift?For this problem, you don't really need to know sigma and mu. You can just use them as variables and they cancel out. In the lectures we derived a formula for type one error: a = pr(x > p + ko, or x