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 and variances 012, 022, and 03, respectively. (Round your answers to four decimal places.) USE SALT (a) If 1 M2 = 3 = 70 and 1 P(T 228) = P(174 To 228) = 2 2 2 = 02 = 03 = 18, calculate P(T 228) and P(174 To 228). (b) Using the 's and oi's given in part (a), calculate both P(64 X) and P(68 X 72). P(64 X) P(68 X 72) = = (c) Using the i'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) = 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 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. The quantity represents the probability that the difference between X1 and the average of X2 and X3 is between -12 and 6. 2 (d) If = 30, 2 = 40, 3 = 50, 01 = 14, 02 = 10, and 03 = 12, calculate P(X + X2 + X3 132) and also P(X1 + X2 2X3). P(X1 + x2 + X3 132) = P(X1 + x2 2X3) = You may need to use the appropriate table in the Appendix of Tables to answer this question.