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DS212_HW7_Solutions

# DS212_HW7_Solutions - DS 212 Business Statistics Soorapanth...

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DS 212 Business Statistics Soorapanth Homework #7: Chapter 7 Sampling and Sampling Distributions 7.14 µ = 23.45 σ = 3.8 a) n = 10, P ( x > 22): z = 10 8 . 3 45 . 23 22 - = - n x σ μ = -1.21 from Table A.5, prob. = .3869 P ( x > 22) = .3869 + .5000 = .8869 b) n = 4, P ( x > 26): z = 4 8 . 3 45 . 23 26 - = - n x σ μ = 1.34 from Table A.5, prob. = .4099 P ( x > 26) = .5000 - .4099 = .0901 7.15 n = 36 µ = 278 P ( x < 280) = .86 .3600 of the area lies between x = 280 and µ = 278. This probability is associated with z = 1.08 from Table A.5. Solving for σ : z = n x σ μ - 1.08 = 36 278 280 σ - 1.08 6 σ = 2 1

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DS 212 Business Statistics Soorapanth σ = 08 . 1 12 = 11.11 7.17 a) N = 1,000 n = 60 µ = 75 σ = 6 P ( x < 76.5): z = 1 1000 60 1000 60 6 75 5 . 76 1 - - - = - - - N n N n x σ μ = 2.00 from Table A.5, prob. = .4772 P ( x < 76.5) = .4772 + .5000 = .9772 b) N = 90 n = 36 µ = 108 σ = 3.46 P (107 < x < 107.7): z = 1 90 36 90 36 46 . 3 108 107 1 - - - = - - - N n N n x σ μ = -2.23 from Table A.5, prob. = .4871 z = 1 90 36 90 36 46 . 3 108 7 . 107 1 - - - = - - - N n N n x σ μ = -0.67 from Table A.5, prob. = .2486 P (107 < x < 107.7) = .4871 - .2486 = .2385 c) N = 250 n = 100 µ = 35.6 σ = 4.89 P ( x > 36): z = 1 250 100 250 100 89 . 4 6 . 35 36 1 - - - = - - - N n N n x σ μ = 1.05 from Table A.5, prob. = .3531 2
DS 212 Business Statistics Soorapanth P ( x > 36) = .5000 - .3531 = .1469 d) N = 5000 n = 60 µ = 125 σ = 13.4 P ( x < 123): z = 1 5000 60 5000 60 4 . 13 125 123 1 - - - = - - - N n N n x σ μ = -1.16 from Table A.5, prob. = .3770 P ( x < 123) = .5000 - .3770 = .1230 7.18 µ = 99.9 σ = 30 n = 38 a) P ( x < 90): z = 38 30

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