a. Explanation Calculation: It is given that due to uncertainties in financial resources, the project completion time has not been set. The proportion of completion within one year follows a beta distribution with the parameters α = 1 , β = 5 . Beta distribution: If X follows beta distribution then the probability density function of X is, f ( x ) = Γ ( α + β ) Γ ( α ) Γ ( β ) x α − 1 ( 1 − x ) β − 1 , for x in [ 0 , 1 ] , α , β > 0 , with mean E ( X ) = α α + β and variance V ( X ) = α β ( α + β ) 2 ( α + β + 1 ) . Let X be the proportion of completion within one year b. To determine Find the probability that more than half of the project is completed within one year. c. To determine Find the proportion of the project that is completed within one year with probability 0.9.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 4, Problem 219SE

To determine

Find the mean and the variance of the proportion completed within one year.

To determine

Find the probability that more than half of the project is completed within one year.

To determine

Find the proportion of the project that is completed within one year with probability 0.9.

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Chapter 4, Problem 218SE

Chapter 4, Problem 221SE

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Chapter 4 Solutions

Applied Statistics and Probability for Engineers

Ch. 4.2 - 4-1. Suppose that f(x) = e−x for 0 < x. Determine...Ch. 4.2 - 4-2. Suppose that f (x) = 3(8x – x2)/256 for 0< x...Ch. 4.2 - 4-3. Suppose that f (x) = 0.5 cos x for −π/2 < x <...Ch. 4.2 - Prob. 4E Ch. 4.2 - 4-5. Go Tutorial Suppose that for 3 < x < 5....Ch. 4.2 - Prob. 6E Ch. 4.2 - 4-7. Suppose that f(x) = 1 .5x2 for −1 < x < 1....Ch. 4.2 - 4-8. The probability density function of the time...Ch. 4.2 - 4-9. The probability density function of the net...Ch. 4.2 - Prob. 10E

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