ISM_Chapter_08

ISM_Chapter_08 - Chapter 8 8.1a P(30 < X < 45) 15 400...

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Unformatted text preview: Chapter 8 8.1a P(30 < X < 45) 15 400 146 ) 30 45 ( × ×- ≈ = .365 b P(90 < X < 120) 15 400 6 ) 105 120 ( 15 400 11 ) 90 105 ( × ×- + × ×- ≈ = .0425 c P(40 < X < 80) 15 400 24 ) 75 80 ( 15 400 68 ) 60 75 ( 15 400 110 ) 45 60 ( 15 400 146 ) 40 45 ( × ×- + × ×- + × ×- + × ×- ≈ = .5867 d P(X > 100) 0342 . 15 400 1 ) 150 165 ( 15 400 ) 135 150 ( 15 400 3 ) 120 135 ( 15 400 6 ) 105 120 ( 15 400 11 ) 100 105 ( = × ×- + × ×- + × ×- + × ×- + × ×- ≈ 8.2 a P(X > 45) 15 50 2 ) 60 75 ( 15 50 2 ) 45 60 ( × ×- + × ×- ≈ = .0800 b P(10 < X < 40) 15 50 6 ) 30 40 ( 15 50 7 ) 15 30 ( 15 50 17 ) 10 15 ( × ×- + × ×- + × ×- ≈ = .3333 c P(X < 25) 15 50 7 ) 15 25 ( 15 50 17 ) 15 ( 15 50 10 ]) 15 [ ( 15 50 6 ]) 30 [ 15 ( × ×- + × ×- + × ×-- + × ×--- ≈ = .7533 d P(35 < X < 65) 15 50 2 ) 60 65 ( 15 50 2 ) 45 60 ( 15 50 6 ) 35 45 ( × ×- + × ×- + × ×- ≈ = .1333 8.3 a P(55 < X < 80) 10 60 24 ) 70 80 ( 10 60 5 ) 60 70 ( 10 60 16 ) 55 60 ( × ×- + × ×- + × ×- ≈ = .6167 b P(X > 65) 10 60 1 ) 90 100 ( 10 60 7 ) 80 90 ( 10 60 24 ) 70 80 ( 10 60 5 ) 65 70 ( × ×- + × ×- + × ×- + × ×- ≈ = .5750 c P(X < 85) 10 60 7 ) 80 85 ( 10 60 24 ) 70 80 ( 10 60 5 ) 60 70 ( 10 60 16 ) 50 60 ( 10 60 7 ) 40 50 ( × ×- + × ×- + × ×- + × ×- + × ×- ≈ = .9250 d P(75 < X < 85) 10 60 7 ) 80 85 ( 10 60 24 ) 75 80 ( × ×- + × ×- ≈ = .2583 183 8.4 a b P(X > 25) = 0 c P(10 < X < 15) = 20 1 ) 10 15 (- = .25 d P(5.0 < X < 5.1) = 20 1 ) 5 1 . 5 (- = .005 8.5 a f(x) = ) 20 60 ( 1- = 40 1 20 < x < 60 b P(35 < X < 45) = (45–35) 40 1 = .25 184 c 8.6 f(x) = 30 1 ) 30 60 ( 1 =- 30 < x < 60 a P(X > 55) = 30 1 ) 55 60 (- = .1667 b P(30 < X < 40) = 30 1 ) 30 40 (- = .3333 c P(X = 37.23) = 0 8.7 5 . 7 ) 30 60 ( 4 1 =- × ; The first quartile = 30 + 7.5 = 37.5 minutes 8.8 3 ) 30 60 ( 10 . =- × ; The top decile = 60–3 = 57 minutes 8.9 f(x) = 65 1 ) 110 175 ( 1 =- 110 < x < 175 a P(X > 150) = 65 1 ) 150 175 (- = .3846 b P(120 < X < 160) = 65 1 ) 120 160 (- = .6154 8.10 .20(175–110) = 13. Bottom 20% lie below (110 + 13) = 123 For Exercises 8.11 to 8.14 we calculate probabilities by determining the area in a triangle. That is, Area in a triangle = (.5)(height)(base) 185 8.11 a b P(0 < X < 2) = (.5)(2–0)(1) = 1.0 c P(X > 1) = (.5)(2 – 1)(.5) = .25 d P(X < .5) = 1 – P(X > .5) = 1 – (.5)(.75)(2–.5) = 1 – .5625 = .4375 e P(X = 1.5) = 0 8.12 a b P(2 < X < 4) = P(X < 4) – P(X < 2) = (.5)(3/8)(4–1) – (.5)(1/8)(2–1) = .5625 – .0625 = .5 c P(X < 3) = (.5)(2/8)(3–1) = .25 186 8.13a b P(1 < X < 3) = P(X < 3) – P(X < 1) = ) 1 ( 25 1 2 1 ) 3 ( 25 3 2 1- × ×-- × × = .18 – .02 = .16 c P(4 < X < 8) = P(4 < X < 5) + P(5 < X < 8) P(4 < X < 5)= P(X < 5) – P(X <4) = ) 4 ( 25 4 2 1 ) 5 ( 25 5 2 1- × ×-- × × = .5 – .32 = .18 P(5 < X < 8) = P(X > 5) – P(X > 8) = ) 8 10 ( 25 2 2 1 ) 5 10 ( 25 5 2 1- × ×-- × × = .5 – .08 = .42 P(4 < X < 8) = .18 + .42 = .60 d P(X < 7) = 1 – P(X > 7) P(X > 7) = ) 7 10 (...
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This note was uploaded on 04/09/2008 for the course OMIS 41 taught by Professor Schaffzin,richard during the Spring '08 term at Santa Clara.

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ISM_Chapter_08 - Chapter 8 8.1a P(30 < X < 45) 15 400...

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