Chapter 08 - 136 Chapter 8 8.1a P(30 < X < 45) 15 400...

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136 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) 15 400 1 ) 150 165 ( 15 400 0 ) 135 150 ( 15 400 3 ) 120 135 ( 15 400 6 ) 105 120 ( 15 400 11 ) 100 105 ( ´ ´ - + ´ ´ - + ´ ´ - + ´ ´ - + ´ ´ - » = .0342 8.2 a P(X > 45) 15 50 2 ) 60 75 ( 15 50
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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 ) 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 8.3 a P(55 < X < 80) 10 60 24 ) 70 80 ( 10 60 5 ) 60 70 ( 10 60 16 ) 55 60 ( ´ ´ - + ´ ´ - +
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´ ´ - » = .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 8.4 a 137 b P(X > 25) = 0 c P(10 < X < 15) = 20 1 ) 10 15 ( - = .25 d P(5.0 < X < 5.1) = 20
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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 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 138 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 8.11 a c P(X > 1) = (.5)(2 & 1)(.5) = .25 d P(X < .5) = 1 k P(X > .5) = 1 H (.75)(1.5)(.5) = 1 - .5625 = .4375
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e P(X = 1.5) = 0 8.12 a 0625 = .5 c P(X < 3) = (2)(2/8)(.5) = .25 8.13a 139 b P(1 < X < 3) = P(X < 3) ² 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 P(X > 8) = ) 8 10 ( 25 2 2 1 ) 5 10 ( 25 5 2 1 - ´ ´ - - ´ ´ = .5 - .08 = .42 P(4 < X < 8) = .42 + .18 = .60 d P(X < 7) = 1 & P(X > 7) P(X > 7) = ) 7 10 ( 25 3 2 1 - ´ ´ = .18 P(X < 7) = 1 - .18 = .82 e P(X > 3) = 1 & P(X < 3) P(X < 3) = ) 0 3 ( 25 3 2 1 - ´ ´ = .18 P(X > 3) = 1 - .18 = .82 8.14 a f(x) = .10 - .005x 0 £ x £ 20
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Chapter 08 - 136 Chapter 8 8.1a P(30 &lt; X &lt; 45) 15 400...

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