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 μ₁, μ₂, and μ3 and variances σ₁ ², σ22, and σ32, respectively. (Round your answers to four decimal places.) USE SALT 02 (a) If μ₁ = μ₂ = μ3 = 80 and σ. 2 101° = 2 = 02 03 2 = 15, calculate P(T ≤ 255) and P(210 ≤ To ≤ 255). P(T ≤ 255) = 0.5944 P(210 ≤ To ≤ 255) = (b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82). (c) P(75 ≤ X) P(78 ≤ X ≤ 82) S = = Using the μ's and σ's given in part (a), calculate P(-10 ≤ X₁ - 0.5X2 - 0.5X3 ≤ 5). - P(-10 ≤ X₁ = 0.5X2 - 0.5X3 ≤ 5) S = Interpret the quantity P(-10 ≤ X₁1 - 0.5X2 - 0.5X3 ≤ 5). (d) If μ1 The quantity represents the probability that X1, X2, and X3 are all between -10 and 5. The quantity represents the probability that the difference between ✗₁ and the average of X2 and X3 is between -10 and 5. ○ The quantity represents the probability that the difference between X₁ and the sum of X2 and X3 is between -10 and 5. 1 ○ The quantity represents the probability that the difference between X3 and the sum of X₁ and X2 is between -10 and 5. ○ The quantity represents the probability that the difference between X 3 and the average of X1 and X2 is between -10 and 5. 2 2 = 50, μ2 = 60, μ3: 70, σ₁² = 10, σ2² = 14, and σ3² = 12, calculate P(X ₁ + X2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). P(X1 + x2 + X3 ≤ 190) = 03 P(x1 + x2 ≥ 2X3) = You may need to use the appropriate table in the Appendix of Tables to answer this question.