By Douglas C. Montgomery, George C. Runger
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Additional resources for Applied Statistics and Probability for Engineers. Student Solutions Manual
The joint probability distribution is not necessary because the two processes are independent and we can just multiply the probabilities. Section 5-4 0. 5 1 1 5-55. 0625 c) P(Z < 2) = 1, because the range of Z is from 0 to 1. 5, Z < 2). 5). Therefore, the answer is 1. 1 1 1 e) 1 E ( X ) = ∫ ∫ ∫ (8 x yz )dzdydx = ∫ (2 x 2 )dx = 2 0 0 0 2 x3 3 = 2/3 0 1 5-57. a) fYZ ( y, z ) = ∫ (8 xyz )dx = 4 yz for 0 < y < 1 and 0 < z < 1. 8) fYZ ( y, z ) for 0 < x < 1. 25 0 5-61 Determine c such that f ( xyz ) = c is a joint density probability over the region x>0, y>0 and z>0 with x+y+z<1 1 1− x 1− x − y 1 1− x 1 0 0 0 0 0 f ( xyz ) = c ∫ ∫ ∫ dzdydx =∫ ∫ c(1 − x − y )dydx = ∫ 0 1 (1 − x) 2 = ∫ c (1 − x) − x(1 − x) − 2 0 1 = c .
4, based on Table IV. Minitab gives P-value = 1. 75. 75), n * = 75 . 9-41 Therefore, n= n * + 1 75 + 1 = = 38 2 2 and n=38. a) In order to use t statistics in hypothesis testing, we need to assume that the underlying distribution is normal. 1) The parameter of interest is the true mean concentration of suspended solids, µ. 05. 005. 2. 8. d) From the same OC chart, and for the specified power, we would need approximately 38 observations. d= n * = 75 . 90), n * + 1 75 + 1 = = 38 2 2 and n=38. Section 9-4 9-43 a) In order to use the χ2 statistic in hypothesis testing and confidence interval construction, we need to assume that the underlying distribution is normal.
3962 The degrees of freedom are k − p − 1 = 3 − 1 − 1 = 1 a) 1) The variable of interest is the form of the distribution for the number of under-filled cartons, X. 05,1 = 384 . 053 381426 . 84 do not reject H0. 05. 3048 (found using Minitab) Section 9-8 9-65. 1. The variable of interest is breakdowns among shift. 2. H0: Breakdowns are independent of shift. 3. H1: Breakdowns are not independent of shift. 4. 05 5. The test statistic is: r c χ = ∑∑ 2 0 (O − Eij ) 2 ij Eij i =1 j =1 6. 65 2 7. 8. 05.
Applied Statistics and Probability for Engineers. Student Solutions Manual by Douglas C. Montgomery, George C. Runger
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