# Chapter 8 - Chapter 8 8.1a P(X > 45(60 45 2(75 60 2 = 50...

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Chapter 8 8.1a. P(X > 45) 15 50 2 ) 60 75 ( 15 50 2 ) 45 60 ( × × - + × × - = .0800 b. P(10 < X < 40) 15 50 8 ) 30 40 ( 15 50 8 ) 15 30 ( 15 50 16 ) 10 15 ( × × - + × × - + × × - = .4800 c. P(X < 25) 15 50 7 ) 15 25 ( 15 50 17 ) 0 15 ( 15 50 10 ]) 15 [ 0 ( 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 8.2a. P(X > 45) 15 50 3 ) 60 75 ( 15 50 3 ) 45 60 ( × × - + × × - = .1200 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 8 ) 15 25 ( 15 50 16 ) 0 15 ( 15 50 2 ]) 15 [ 0 ( 15 50 5 ]) 30 [ 15 ( 15 50 5 ]) 45 [ 30 ( × × - + × × - + × × - - + × × - - - + × × - - - = .6667 d. P(35 < X < 65) 15 50 3 ) 60 65 ( 15 50 3 ) 45 60 ( 15 50 8 ) 35 45 ( × × - + × × - + × × - = .1867 8.3a. 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 199

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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 8.5a. f(x) = ) 20 60 ( 1 - = 40 1 20 < x < 60 b. P(35 < X < 45) = (45–35) 40 1 = .25 200
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) 201

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8.11a. 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) = .25 202
8.13a. b. P(1 < X < 3) = P(X < 3) – P(X < 1) = ) 0 1 ( 25 1 2 1 ) 0 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) = ) 0 4 ( 25 4 2 1 ) 0 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)

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Chapter 8 - Chapter 8 8.1a P(X > 45(60 45 2(75 60 2 = 50...

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