ch06 e SOLUTION.doc - Chapter 6 Continuous Distributions 1...

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Chapter 6: Continuous Distributions 1 Chapter 6 Continuous Distributions SOLUTIONS TO PROBLEMS IN CHAPTER 6 Ans Not included: 8, 12, 16, 23 6.1 a = 200 b = 240 a) f(x) = 40 1 200 240 1 1 a b b) = 2 240 200 2 b a = 220 = 12 40 12 200 240 12 a b = 11.547 c) P(x> 230) = 40 10 200 240 230 240 = .250 d) P(205 < x < 220) = 40 15 200 240 205 220 = .375 e) P(x < 225) = 40 25 200 240 200 225 = .625 6.2 a = 8 b = 21 a) f(x) = 13 1 8 21 1 1 a b b) = 2 29 2 21 8 2 b a = 14.5 = 12 13 12 8 21 12 a b = 3.7528 c) P(10 < x < 17) = 13 7 8 21 10 17 = .5385 d) P(x > 22) = .0000 e) P(x > 7) = 1.0000 6.3 a = 2.80 b = 3.14 = 2 14 . 3 80 . 2 2 b a = 2.97 = 12 80 . 2 14 . 3 12 a b = 0.10 P(3.00 < x < 3.10) = 80 . 2 14 . 3 00 . 3 10 . 3 = 0.2941 6.4 a = 11.97 b = 12.03 Height = 97 . 11 03 . 12 1 1 a b = 16.667 P(x > 12.01) = 97 . 11 03 . 12 01 . 12 03 . 12 = .3333 P(11.98 < x < 12.01) = 97 . 11 03 . 12 98 . 11 01 . 12 = .5000 6.5 µ = 2100 a = 400 b = 3800 = 12 400 3800 12 a b = 981.5 Height = 12 400 3800 1 a b = .000294 P(x > 3000) = 3400 800 400 3800 3000 3800 = .2353 P(x > 4000) = .0000 P(700 < x < 1500) = 3400 800 400 3800 700 1500 = .2353 6.6 a) Prob(x < 635 µ = 604, = 56.8): z = 8 . 56 604 635 x = 0.55 Table A.5 value for z = 0.55: .2088 Prob(x < 635) = .2088 + .5000 = .7088 b) Prob(x < 20 µ = 48, = 12): z = 12 48 20 x = -2.33 Table A.5 value for z = -2.33: .4901 Prob(x < 20) = .5000 - .4901 = .0099 c) Prob(100 < x < 150 µ = 111, = 33.8): z = 8 . 33 111 150 x = 1.15 Table A.5 value for z = 1.15: .3749 z = 8 . 33 111 100 x = -0.33 Table A.5 value for z = -0.33: .1293 Prob(100 < x < 150) = .3749 + .1293 = .5042
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Chapter 6: Continuous Distributions 2 d) Prob(250 < x < 255 µ = 264, = 10.9): z = 9 . 10 264 250 x = -1.28 Table A.5 value for z = -1.28: .3997 z = 9 . 10 264 255 x = =0.83 Table A.5 value for z = -0.83: .2967 Prob(250 < x < 255) = .3997 - .2967 = .1030 e) Prob(x > 35 µ = 37, = 4.35): z = 35 . 4 37 35 x = -0.46 Table A.5 value for z = -0.46: .1772 Prob(x > 35) = .1772 + .5000 = .6772 f) Prob(x > 170 µ = 156, = 11.4): z = 4 . 11 156 170 x = 1.23 Table A.5 value for z = 1.23: .3907 Prob(x > 170) = .5000 - .3907 = .1093 6.7 µ = 22 = 4 a) Prob( x > 17): z = 4 22 17 x = -1.25 area between x = 17 and µ = 22 from table A.5 is .3944 Prob( x > 17) = .3944 + .5000 = .8944 b) Prob( x < 13): z = 4 22 13 x = -2.25 from table A.5, area = .4878 Prob( x < 13) = .5000 - .4878 = .0122 c) P(25 < x < 31): z = 4 22 31 x = 2.25 from table A.5, area = .4878 z = 4 22 25 x =0.75 from table A.5, area = .2734 Prob(25 < x < 31)=.4878 -.2734= .2144 6.9 µ = $1332 = $575 a) Prob(x > $2000): z = 725 1332 2000 x = 0.92 from Table A.5, the z = 0.92 yields: .3212 Prob(x > $2000) = .5000 - .3212 = .1788 b) Prob(owes money) = Prob(x < 0): z = 725 1332 0 x = -1.84 from Table A.5, the z = -1.84 yields: .4671 Prob(x < 0) = .5000 - .4671 = .0329 c) Prob($100 < x < $700): z = 725 1332 100 x = -1.70 from Table A.5, the z = -1.70 yields: .4554 z = 725 1332 700 x = -0.87 from Table A.5, the z = -0.87 yields: .3078 Prob($100 < x < $700) = .4554 - .3078 = .1476 6.10 = $30,000 = $9,000 a) Prob($15,000 < x < $45,000): z = 000 , 9 000 , 30 000 , 45 x = 1.67 From Table A.5, z = 1.67 yields: .4525 z = 000 , 9 000 , 30 000 , 15 x = -1.67 From Table A.5, z = -1.67 yields: .4525 Prob($15,000 < x < $45,000) = .4525 + .4525 = .9050 b) Prob(x > $50,000): z = 000 , 9 000 , 30 000 , 50 x = 2.22 From Table A.5, z = 2.22 yields: 4868 Prob(x > $50,000) = .5000 - .4868 = .0132 c) Prob($5,000 < x < $20,000): z = 000 , 9 000 , 30 000 , 5 x = -2.78
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Chapter 6: Continuous Distributions 3 From Table A.5, z = -2.78 yields: .4973 z = 000 , 9 000 , 30 000 , 20 x = -1.11 From Table A.5, z = -1.11 yields .3665 Prob($5,000 < x < $20,000) = .4973 - .3665 = .1308 d) 90.82% of the values are greater than x = $7,000. Then x = $7,000 is in the lower half of the distribution and .9082 - .5000 = .4082 lie between x and µ. From Table A.5, z = -1.33 is associated with an area of .4082.
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