1 The number of times a certain factory machine breaks down each working week has been recorded over a long period. From these data, the following probability distribution for the number, X, of weekly breakdowns was produced. x 0 2 4 5 6 P(X = x) 0.04 0.24 0.28 0.16 0.16 0.08 0.04 (a) Find the mean and standard deviation of X. (b) What would be the expected total number of breakdowns that will occur over the next 48 working weeks