Suppose that the manufacturing of a particular part requires three different machining operations. Machining time (X1, X2, X3) for each of the three operations has a normal distribution and are independent from one another. The mean values are 10, 12, and 8 minutes respectively, and standard deviations are 2, 2.5, and 1.5 respectively. a) What is the probability that it takes at most 26 minutes total to produce a randomly selected part? b) What is the probability the difference in machining timing between the second and first operation (X2-X1) exceeds 6 minutes?

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