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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, M2, and variances o₁2, 02², and σ3², respectively. (Round your answers to four decimal places.) 1 2 and I USE SALT 2 2 = 15, calculate P(To ≤ 255) and P(210 ≤ T。 ≤ 255). (a) If μ₁ = μ₂ = μ3 = 80 and σ₁² 1 ² = 0 2 ² = 0 3 ² P(T。 ≤ 255) = P(210 T255) = (b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82). P(75 ≤ X) = P(78 ≤ X ≤ 82) = (c) 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) = - - Interpret the quantity P(−10 ≤ X₁ − 0.5X2 − 0.5X3 ≤ 5). 1 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 X₁ 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. 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 X3 and the average of X1 and X2 is between -10 and 5. (d) If M1 = 50, μ₂ = 60, μ3 = 70, σ₁² 2 = 10,022 2 = 14, and σ3² = 12, calculate P(X₁ + X2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = μ3

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, M2, and variances o₁2, 02², and σ3², respectively. (Round your answers to four decimal places.) 1 2 and I USE SALT 2 2 = 15, calculate P(To ≤ 255) and P(210 ≤ T。 ≤ 255). (a) If μ₁ = μ₂ = μ3 = 80 and σ₁² 1 ² = 0 2 ² = 0 3 ² P(T。 ≤ 255) = P(210 T255) = (b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82). P(75 ≤ X) = P(78 ≤ X ≤ 82) = (c) 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) = - - Interpret the quantity P(−10 ≤ X₁ − 0.5X2 − 0.5X3 ≤ 5). 1 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 X₁ 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. 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 X3 and the average of X1 and X2 is between -10 and 5. (d) If M1 = 50, μ₂ = 60, μ3 = 70, σ₁² 2 = 10,022 2 = 14, and σ3² = 12, calculate P(X₁ + X2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = μ3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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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, M2, and variances o₁2, 02², and σ3², respectively. (Round your answers to four decimal places.) 1 2 and I USE SALT 2 2 = 15, calculate P(To ≤ 255) and P(210 ≤ T。 ≤ 255). (a) If μ₁ = μ₂ = μ3 = 80 and σ₁² 1 ² = 0 2 ² = 0 3 ² P(T。 ≤ 255) = P(210 T255) = (b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82). P(75 ≤ X) = P(78 ≤ X ≤ 82) = (c) 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) = - - Interpret the quantity P(−10 ≤ X₁ − 0.5X2 − 0.5X3 ≤ 5). 1 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 X₁ 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. 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 X3 and the average of X1 and X2 is between -10 and 5. (d) If M1 = 50, μ₂ = 60, μ3 = 70, σ₁² 2 = 10,022 2 = 14, and σ3² = 12, calculate P(X₁ + X2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = μ3
Transcribed Image Text: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, M2, and variances o₁2, 02², and σ3², respectively. (Round your answers to four decimal places.) 1 2 and I USE SALT 2 2 = 15, calculate P(To ≤ 255) and P(210 ≤ T。 ≤ 255). (a) If μ₁ = μ₂ = μ3 = 80 and σ₁² 1 ² = 0 2 ² = 0 3 ² P(T。 ≤ 255) = P(210 T255) = (b) Using the μ's and σ's given in part (a), calculate both P(75 ≤ X) and P(78 ≤ X ≤ 82). P(75 ≤ X) = P(78 ≤ X ≤ 82) = (c) 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) = - - Interpret the quantity P(−10 ≤ X₁ − 0.5X2 − 0.5X3 ≤ 5). 1 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 X₁ 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. 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 X3 and the average of X1 and X2 is between -10 and 5. (d) If M1 = 50, μ₂ = 60, μ3 = 70, σ₁² 2 = 10,022 2 = 14, and σ3² = 12, calculate P(X₁ + X2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = μ3
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