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DS212_HW6_Solutions

# DS212_HW6_Solutions - DS 212 Business Statistics Soorapanth...

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DS 212 Business Statistics Soorapanth Homework #6: Chapter 6 Continuous Distributions 6.2 a = 8 b = 21 a) f ( x ) = = .0769 b) μ = = 14.5 σ = = 3.7528 c) P (10 < x < 17) = = .5385 d) P ( x > 22) = .0000 e) P ( x > 7) = 1.0000 1

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DS 212 Business Statistics Soorapanth 6.3 a = 2.80 b = 3.14 μ = = 2.97 σ = = 0.098 P (3.00 < x < 3.10) = = 0.2941 6.5 µ = 2100 a = 400 b = 3800 σ = = 981.5 Height = = .000294 P ( x > 3000) = = .2353 P ( x > 4000) = .0000 P (700 < x < 1500) = = .2353 6.6 a) P ( x < 635 µ = 604, σ = 56.8): z = = 0.55 Table A.5 value for z = 0.55: .2088 P ( x < 635) = .2088 + .5000 = .7088 2
DS 212 Business Statistics Soorapanth b) P ( x < 20 µ = 48, σ = 12): z = = -2.33 Table A.5 value for z = -2.33: .4901 P ( x < 20) = .5000 - .4901 = .0099 c) P (100 < x < 150 µ = 111, σ = 33.8): z = = 1.15 Table A.5 value for z = 1.15: .3749 z = = -0.33 Table A.5 value for z = -0.33: .1293 P (100 < x < 150) = .3749 + .1293 = .5042 d) P (250 < x < 255 µ = 264, σ = 10.9): z = = -1.28 Table A.5 value for z = -1.28: .3997 z = = -0.83 Table A.5 value for z = -0.83: .2967 P (250 < x < 255) = .3997 - .2967 = .1030 3

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DS 212 Business Statistics Soorapanth e) P ( x > 35 µ = 37, σ = 4.35): z = = -0.46 Table A.5 value for z = -0.46: .1772 P ( x > 35) = .1772 + .5000 = .6772 f) P ( x > 170 µ = 156, σ = 11.4): z = = 1.23 Table A.5 value for z = 1.23: .3907 P ( x > 170) = .5000 - .3907 = .1093 6.8 µ = 60 σ = 11.35 a) P ( x > 85): z = = 2.20 from Table A.5, the value for z = 2.20 is .4861 P ( x > 85) = .5000 - .4861 = .0139 b) P (45 < x < 70): z = = -1.32 z = = 0.88 from Table A.5, the value for z = -1.32 is .4066 and for z = 0.88 is .3106 4
DS 212 Business Statistics Soorapanth P (45 < x < 70) = .4066 + .3106 = .7172 5

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DS 212 Business Statistics Soorapanth c) P (65 < x < 75): z = = 0.44 z = = 1.32 from Table A.5, the value for z = 0.44 is .1700 from Table A.5, the value for z = 1.32 is .4066 P (65 < x < 75) = .4066 - .1700 = .2366 d) P ( x < 40): z = = -1.76 from Table A.5, the value for z = -1.76 is .4608 P ( x < 40) = .5000 - .4608 = .0392 6.9 µ = \$1332 σ = \$725 a) P ( x > \$2000): z = = 0.92 from Table A.5, the z = 0.92 yields: .3212 P ( x > \$2000) = .5000 - .3212 = .1788 b) P (owes money) = P ( x < 0): z = = -1.84 6
DS 212 Business Statistics Soorapanth from Table A.5, the z = -1.84 yields: .4671 P ( x < 0) = .5000 - .4671 = .0329 c) P (\$100 < x < \$700): z = = -1.70 from Table A.5, the z = -1.70 yields: .4554 z = = -0.87 from Table A.5, the z = -0.87 yields: .3078 P

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DS212_HW6_Solutions - DS 212 Business Statistics Soorapanth...

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