Explanation Calculation: It is given that for completing one task, the maximum time is 2.5 days. The proportion completion time follows a beta distribution with the parameters α = 2 , β = 3 . 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 completion proportion of the maximum time. Here, the proportion is 2 days 2.5 days = 0.8 The probability that the given task requires more than two days to complete: P ( X > 0.8 ) = ∫ 0.8 1 Γ ( α + β ) Γ ( α ) Γ ( β ) x α − 1 ( 1 − x ) β − 1 d x = Γ ( 2 + 3 ) Γ ( 2 ) Γ ( 3 ) ∫ 0.8 1 x 2 − 1 ( 1 − x ) 3 − 1 d x , substituting , α = 2 , β = 3 = Γ ( 5 ) Γ ( 2 ) Γ ( 3 ) ∫ 0

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 4.12, Problem 189E

To determine

Find the probability that the given task requires more than two days to complete.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.12, Problem 188E

Chapter 4.12, Problem 190E

Students have asked these similar questions

You assume that the annual incomes for certain workers are normal with a mean of $28,500 and a standard deviation of $2,400. What’s the chance that a randomly selected employee makes more than $30,000?What’s the chance that 36 randomly selected employees make more than $30,000, on average?

What’s the chance that a fair coin comes up heads more than 60 times when you toss it 100 times?

Suppose that you have a normal population of quiz scores with mean 40 and standard deviation 10. Select a random sample of 40. What’s the chance that the mean of the quiz scores won’t exceed 45?Select one individual from the population. What’s the chance that his/her quiz score won’t exceed 45?

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

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.