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 #₁, #2, and and variances ₂², ₂2, and o3², respectively. (Round your answers to four decimal places.) USE SALT (a) If μ₁ = H₂ = H3 = 60 and ₁² = 6₂² = 63² = 18, calculate P(T≤ 198) and P(144 ≤ T ≤ 198). P(T ≤ 198) = P(144 ≤ T ≤ 198) = X (b) Using the μ's and ai's given in part (a), calculate both P(54 ≤X) and P(58 < X < 62). P(54 ≤ X) = X P(58 ≤ x ≤ 62) = (c) Using the μ's and oi's given in part (a), calculate P(-12 ≤ X₁-0.5X₂ - 0.5X3 ≤ 6). P(-12 ≤ X₁0.5X₂ - 0.5X3 ≤ 6) = Interpret the quantity P(-12 ≤ X₁ -0.5X₂ - 0.5X3 ≤ 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 X3 and the sum of X₁ and X₂ is between -12 and 6. The quantity represents the probability that X₁, X₂, and X3 are all between -12 and 6. O The quantity represents the probability that the difference between X₁ and the average of X₂ and X3 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. (d) If μ₁ = 50, H₂ = 60, H3 = 70, 0₁2 = 12, 0₂2 = 10, and 32 = 14, calculate P(X₁ + X₂ + X3 ≤ 192) and also P(X₁ + X₂ 2 2X3). P(X₁ + X₂ + X3 ≤ 192) =