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 your answers to four decimal places.) ЛUSE SALT (a) If μ₁ = μ₂ = μ3 = 60 and σ₁ P(T。 ≤ 204) = 0.9995 P(144 ≤ T ≤204) = 0.9995 2 2 2 02 = 03 = 18, calculate P(To ≤ 204) and P(144 ≤ T。 ≤ 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) = 0.9215 P(58 ≤ X ≤ 62) S = 0.5858 (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) = 0 Interpret the quantity P(-12 ≤ X₁1 - 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 ✗₁ 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 X and the sum of X2 and X3 is between -12 and 6. 2 1 2 03 (d) If μ₁ = 50, μ₂ = 60, μ3 = 70, σ₁² = 10, σ2² = 14, and σ3² = 12, calculate P(X ₁ + X2 + X3 ≤ 190) and also P(X ₁ + X2 ≥ 2X3). P(X1 + x2 + X3 ≤190) = 0.6832 P(X1 + x2 ≥ 2X3) = 0.1448 M1' M21 and μ3 and variances σ₁2, σ22, and σ3², respectively. (Round
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 your answers to four decimal places.) ЛUSE SALT (a) If μ₁ = μ₂ = μ3 = 60 and σ₁ P(T。 ≤ 204) = 0.9995 P(144 ≤ T ≤204) = 0.9995 2 2 2 02 = 03 = 18, calculate P(To ≤ 204) and P(144 ≤ T。 ≤ 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) = 0.9215 P(58 ≤ X ≤ 62) S = 0.5858 (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) = 0 Interpret the quantity P(-12 ≤ X₁1 - 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 ✗₁ 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 X and the sum of X2 and X3 is between -12 and 6. 2 1 2 03 (d) If μ₁ = 50, μ₂ = 60, μ3 = 70, σ₁² = 10, σ2² = 14, and σ3² = 12, calculate P(X ₁ + X2 + X3 ≤ 190) and also P(X ₁ + X2 ≥ 2X3). P(X1 + x2 + X3 ≤190) = 0.6832 P(X1 + x2 ≥ 2X3) = 0.1448 M1' M21 and μ3 and variances σ₁2, σ22, and σ3², respectively. (Round
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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
your answers to four decimal places.)
ЛUSE SALT
(a) If μ₁ = μ₂ = μ3 = 60 and σ₁
P(T。 ≤ 204)
= 0.9995
P(144 ≤ T ≤204) = 0.9995
2
2
2
02
= 03
=
18, calculate P(To ≤ 204) and P(144 ≤ T。 ≤ 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)
= 0.9215
P(58 ≤ X ≤ 62)
S
= 0.5858
(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) = 0
Interpret the quantity P(-12 ≤ X₁1 - 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 ✗₁ 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 X and the sum of X2 and X3 is between -12 and 6.
2
1
2
03
(d) If μ₁ = 50, μ₂ = 60, μ3 = 70, σ₁² = 10, σ2² = 14, and σ3² = 12, calculate P(X ₁ + X2 + X3 ≤ 190) and also P(X ₁ + X2 ≥ 2X3).
P(X1 + x2 + X3 ≤190) = 0.6832
P(X1 + x2 ≥ 2X3)
= 0.1448
M1'
M21
and
μ3 and variances σ₁2, σ22, and σ3², respectively. (Round
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