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1. Let X₁, X₂, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected values μ₁, ₂, and 3 and variances o,o2, and o3, respectively a) If μ₁=₂=₂= 60 and o² = o2 = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 ≤ x ≤ 62), where X₁ + X₂ + X₂ 3 c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ -0.5X₂-0.5X3 <5). X =

1. Let X₁, X₂, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected values μ₁, ₂, and 3 and variances o,o2, and o3, respectively a) If μ₁=₂=₂= 60 and o² = o2 = 03 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 ≤ x ≤ 62), where X₁ + X₂ + X₂ 3 c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ -0.5X₂-0.5X3 <5). X =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
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1. Let X₁, X₂, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected values µ µ², and µ and variances σ²,02, and o3, respectively a) If μ₁ = μ₂ = μ₂ = 60 and σ² = σ² = 3 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), where X = X₁ + X₂+X3 1 3 c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ −0.5X₂ – 0.5X3 ≤5). d) If µ = 40, µ = 50, µ = 60, o² =10, o² =12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).
Transcribed Image Text:1. Let X₁, X₂, and X3 represent the times necessary to perform three successive repairs tasks at a certain service facility. Suppose they are independent, normal random variables with expected values µ µ², and µ and variances σ²,02, and o3, respectively a) If μ₁ = μ₂ = μ₂ = 60 and σ² = σ² = 3 =15, calculate P(X₁ + X₂ + X3 ≤ 200). b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), where X = X₁ + X₂+X3 1 3 c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ −0.5X₂ – 0.5X3 ≤5). d) If µ = 40, µ = 50, µ = 60, o² =10, o² =12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).
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