A general contracting firm experiences cost overruns on 20% of its contracts. In

Question

A general contracting firm experiences cost overruns on 20% of its contracts. In a company

audit, 20 contracts are sampled at random.

a) what is the probability that the first cost overrun contract is found on the third trial?

b) what is the probability that fewer than three of the 20 contracts experience cost overruns?

c) find the mean and standard deviation of the number of contracts that experience cost overruns.

2. A general contracting firm contracts. In a company audit, 20 experiences cost of its a. are overruns on 20% What is the random. third trial? probability that the first cost overrun contract is found on the b. What is the probability that fewer than three of the 20 contracts experience cost overruns? c. Find the mean and standard deviation of the number of contracts that experience cost overruns.

Explanation / Answer

a)probability that the first cost overrun contract is found on the third trial = 0.8*0.8*0.2 = 0.128

b)probability that fewer than three of the 20 contracts experience cost overruns = P(0)+P(1)+P(2)

= (0.8)20+20*(0.8)19*(0.2)+20C2*(0.8)18*(0.2)2 = 0.2060

c)mean = np = 20*0.2 = 4

variance . = np(1-p) = 20*0.2*0.8 = 3.2

standard deviation = 1.79

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