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 σ12,02², and σ32, respectively. (Round your answers to four decimal places.) Л USE SALT (a) If µ₁ = µ₂ = μ3 = 60 and σ₁ P(T ≤ 204) = P(144 ≤ To ≤204) = 2 2 = ₂² = 0 3² 2 = 18, calculate P(T。 ≤ 204) and P(144 ≤ To ≤ 204). (b) Using the μ's and σ's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62). P(54 ≤ X) = P(58 ≤ X ≤ 62) = (c) Using the μ's and σ;'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 the difference between X3 and the average 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. 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 X3 and the sum of X1 and X2 is between -12 and 6. The quantity represents the probability that the difference between ✗₁ and the sum of X2 and X3 is between -12 and 6. 1 2 10,02 2 (d) If µ₁ = 50, µ₂ = 60, μ3 = 70, σ₁² P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = 2 14, and σ3² = 12, calculate P(X ₁ + X 2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). You may need to use the appropriate table in the Appendix of Tables to answer this question.
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 σ12,02², and σ32, respectively. (Round your answers to four decimal places.) Л USE SALT (a) If µ₁ = µ₂ = μ3 = 60 and σ₁ P(T ≤ 204) = P(144 ≤ To ≤204) = 2 2 = ₂² = 0 3² 2 = 18, calculate P(T。 ≤ 204) and P(144 ≤ To ≤ 204). (b) Using the μ's and σ's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62). P(54 ≤ X) = P(58 ≤ X ≤ 62) = (c) Using the μ's and σ;'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 the difference between X3 and the average 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. 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 X3 and the sum of X1 and X2 is between -12 and 6. The quantity represents the probability that the difference between ✗₁ and the sum of X2 and X3 is between -12 and 6. 1 2 10,02 2 (d) If µ₁ = 50, µ₂ = 60, μ3 = 70, σ₁² P(X 1 + x2 + X3 ≤ 190) = P(X1 + x2 ≥ 2X3) = 2 14, and σ3² = 12, calculate P(X ₁ + X 2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3). You may need to use the appropriate table in the Appendix of Tables to answer this question.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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, μ2, and μ3 and variances σ12,02²,
and σ32, respectively. (Round your answers to four decimal places.)
Л USE SALT
(a) If µ₁ = µ₂ = μ3 = 60 and σ₁
P(T ≤ 204)
=
P(144 ≤ To ≤204) =
2
2
=
₂² = 0 3²
2
=
18, calculate P(T。 ≤ 204) and P(144 ≤ To ≤ 204).
(b) Using the μ's and σ's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62).
P(54 ≤ X) =
P(58 ≤ X ≤ 62) =
(c) Using the μ's and σ;'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 the difference between X3 and the average 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.
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 X3 and the sum of X1 and X2 is between -12 and 6.
The quantity represents the probability that the difference between ✗₁ and the sum of X2 and X3 is between -12 and 6.
1
2
10,02
2
(d) If µ₁ = 50, µ₂ = 60, μ3 = 70, σ₁²
P(X 1 + x2 + X3 ≤ 190)
=
P(X1 + x2 ≥ 2X3)
=
2
14, and σ3² = 12, calculate P(X ₁ + X 2 + X3 ≤ 190) and also P(X₁ + X₂ ≥ 2X3).
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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