Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values , 2, and 3 and variances 12, 022, and 032, respectively. (Round your answers to four decimal places.) USE SALT (a) If 1 2 = 3 = 60 and 1 P(To 198) = 0.6406 P(144 To 198) = 0.6114 2 = 02 2 = 03 2 = 18, calculate P(To 198) and P(144 To 198). (b) Using the 's and oi's given in part (a), calculate both P(54 X) and P(58 X 62). P(54 X) = 0.6293 P(58 X 62) = 0.1766 (c) Using the j's and oi's given in part (a), calculate P(-12 X1 - 0.5X2 - 0.5X3 6). P(-12 X1 -0.5X2 - 0.5X3 6) = 0.7660 Interpret the quantity P(-12 X1 -0.5X2 - 0.5X3 6). The quantity represents the probability that X1, X2, and X3 are all between -12 and 6. The quantity represents the probability that the difference between X and the average of X2 and X3 is between -12 and 6. The quantity represents the probability that the difference between X3 and the sum of X1 and X2 is between -12 and 6. The quantity represents the probability that the difference between X1 and the sum of X2 and X3 is between -12 and 6. The quantity represents the probability that the difference between X3 and the average of X1 and X2 is between -12 and 6. (d) If = 40, 2 = 50, 3 P(X1 + x2 + X3 162) P(X1 + x2 2X3) 2 = 60,01 = 14, 02 = 10, and 03 2 = 12, calculate P(X1 + x2 + X3 162) and also P(X 1 + x2 23). = 0.9772 = 6.1248 Drobabilition should.