A contractor is planning the purchase of equipment, including bulldozers, needed

Question

A contractor is planning the purchase of equipment, including bulldozers, needed for a new project in a remote area. Suppose that from his previous

experience, he figures there is a 60% chance that each bulldozer can last at least 6 months without any breakdown.

a. If he purchased 5 bulldozers, what is the probability that there will be only 1 bulldozer left operative in 6 months?

b. Let X denote the number of operative bulldozers at the end of 6 months.

Whatis the expected number of operating bulldozers at the end of 6 months? And what is the variance and coefficient of variation? State the distribution of X.

Explanation / Answer

Pr ( Each bulldozer will last at least 6 months wthout any breakdown) = 0.6

(a) Purchased 5 bulldozers, that there will be only 1 bulldozer left operative that means other 4 will fail.

so Pr( one bulldozer is operative out of 5 after next 6 monhs) = 5C1 (0.6)1 (1 - 0.6)4 = 0.0768

(b) If X = Number of operative bulldozers at the end of 6 months

Expected number of operating bulldozers = E(X) = = 5 * 0.6 = 3 bulldozers

Varaince of number of operating bulldozers at the end of 6 months 2 = 5 * 0.6 * 0.4 = 1.2

Coefficient of variation C.V = /   = sqrt (1.2)/ 3 = 0.365 = 36.5 %

The distribution of X is a binomial distribution with parameter n = 5 and p = 0.6

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.