Consider a control chart with 3-sigma control limit. (a) What is the probability of a sample being out of control, if the process is actually in-control? (b) What is the probability of four consecutive samples being out of control, if the process is actually in-control? (c) If at time 1, there is a process mean shift of 0.5 sigma (0.5 n), what is the probability of a sample being in control? out of control?