IE360%20HW5%20solutions

IE360%20HW5%20solutions - IE 360 Homework Assignment#5...

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IE 360 Homework Assignment #5 Solutions 7-3 7-4 7-10 8-4 8-6 8-12 8-30 8-37 7-3 psi X 5 . 75 = μ 429 . 1 6 5 . 3 = = = n X σ ( ) 43055 . 0 56945 . 0 1 ) 175 . 0 ( 1 ) 175 . 0 ( ) 75 . 75 ( 429 . 1 5 . 75 75 . 75 / = = = = = Z P Z P P X P n X 7-4 n = 6 n = 49 429 . 1 6 5 . 3 = = = n X 5 . 0 49 5 . 3 = = = n X X is reduced by 0.929 psi 7-10 μ X = 82 . minutes n = 49 σ X = 15 . minutes σ σ μμ X X X X n == = 49 02143 . . . mins Using the central limit theorem, X is approximately normally distributed. a) 1 ) 4 . 8 ( ) 2143 . 0 2 . 8 10 ( ) 10 ( = < = < = < Z P Z P X P
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b) ) ( ) 10 5 ( 2143 . 0 2 . 8 10 2143 . 0 2 . 8 5 < < = < < Z P X P 1 0 1 ) 932 . 14 ( ) 4 . 8 ( = = < < = Z P Z P c) 0 ) 27 . 10 ( ) 2143 . 0 2 . 8 6 ( ) 6 ( = < = < = < Z P Z P X P 8-4 a) 95% CI for 96 . 1 , 1000 20 , 10 , = = = = z x n σ μ 4 . 1012 6 . 987 ) 10 / 20 ( 96 . 1 1000 ) 10 / 20 ( 96 . 1 1000 / / + + n z x n z x b) .95% CI for 96 . 1 , 1000 20 , 25 , = = = = z x n 8 . 1007 2 . 992 ) 25 / 20 ( 96 . 1 1000 ) 25 / 20 ( 96 . 1 1000 / / + + n z x n z x c) 99% CI for 58 . 2 , 1000 20 , 10 , = = = = z x n 3 . 1016 7 . 983 ) 10 / 20 ( 58 . 2 1000 ) 10 / 20 ( 58 . 2 1000 / / + + n z x n z x d) 99% CI for 58 . 2 , 1000 20 , 25 , = = = = z x n 3 . 1010 7 . 989 ) 25 / 20 ( 58 . 2 1000 ) 25 / 20 ( 58 . 2 1000 / / + + n z x n z x e) When n is larger, the CI will get narrower. The higher the confidence level, the wider the
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IE360%20HW5%20solutions - IE 360 Homework Assignment#5...

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