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Chapter_3_Recommended_Homework_Solutions

Chapter_3_Recommended_Homework_Solutions - Chapter 3...

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Chapter 3 Recommended Homework Solutions 3-1. Continuous 3-5. Discrete 3-6. Continuous 3-7. Discrete 3-11. a) P(X > 15) = 1 – P(X 15) = 1 – 0.3 = 0.7 b) P(X 24) = P(X 15) + P(15 < X 24) = 0.3 + 0.6 = 0.9 c) P(15 < X 20) = P(X 20) – P(X 15) = 0.5 – 0.3 = 0.2 d) P(X 18) = P(15 < X 18) + P(X 15) where P(15 < X 18) = P(15 < X 24) – P(18 < X 24) = 0.6 – 0.4 = 0.2 Therefore, P(X 18) = P(15 < X 18) + P(X 15) = 0.2 + 0.3 = 0.5 Alternatively, P(X 18) = P(X 24) - P(18 < X 24) = 0.9 – 0.4 = 0.5. 3-13. a) P(X 7000) = 1 – P(X > 7000) = 1 – 0.45 = 0.55 b) P(X > 5000) = 1 – P(X 5000) = 1 – 0.05 = 0.95 c) P(5000 < X 7000) = P(X 7000) – P(X 5000) = 0.55 – 0.05 = 0.50 3-14. a) Probability that a component does not fail: ) E ( P 1 = 1 – P(E 1 ) = 1 – 0.15 = 0.85 b) P(E 1 or E 2 ) = P(E 1 ) + P(E 2 ) = 0.15 + 0.30 = 0.45 c) P(E 1 or E 2 ) = 1 – 0.45 = 0.55 3-22. a) P(X 2.0080) = 6 . 0 200 0080 . 2 0050 . 2 = dx b) P(X > 2.0055) = 9 . 0 200 0100 . 2 0055 . 2 = dx c) P(2.0080 < X < 2.0090) = 2 . 0 200 0090 . 2 0080 . 2 = dx 3-26. a) E(X) = m 39 . 109 ) 100 ln 120 (ln 600 | ln 600 600 120 100 120 100 2 μ = - = = x dx x x V(X) = 2 2 120 100 2 120 100 2 2 m 19 . 33 39 . 109 | 600 ) ( E 600 μ = - = - x x dx x x b) Average Cost = Coating Cost × Mean of the Coating Thickness = 0.50 × 109.39 = $54.70 3-30. a) P(-z < Z < z) = P(Z < z) – P(Z < -z) = 1 – 2P(Z<-z) = 0.95 So P(Z<-z) = 0.5(1 – 0.95) = 0.025 z = 1.96 b) P(-z < Z < z) = P(Z < z) – P(Z < -z) = 1 – 2P(Z<-z) = 0.99 So P(Z<-z) = 0.5(1 – 0.99) = 0.005 z = 2.58 c) P(-z < Z < z) = P(Z < z) – P(Z < -z) = 1 – 2P(Z<-z) = 0.68 So P(Z<-z) = 0.5(1 – 0.68) = 0.16 z = 1 d) P(-z < Z < z) = P(Z < z) – P(Z < -z) = 1 – 2P(Z<-z) = 0.9973 So P(Z<-z) = 0.5(1 – 0.9973) = 0.00135 z = 3
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3-32. a) P(X > x) = P(Z > z) = 0.5 where z = 2 20 - x = 0. Thus x =20 b) P(X > x) = P(Z > z) = 0.95 where z = 2 20 - x = -1.65. Thus x =16.7 c) P(x < X < 20) = P(Z < 0) – P(Z < z)= 0.5 – P(Z < z) = 0.2 So P(Z < z) = 0.3 where z = 2 20 - x = -0.53. Thus x =18.94
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Chapter_3_Recommended_Homework_Solutions - Chapter 3...

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