Question

A general contracting firm experiences cost overruns on 12% of its contracts. In a company audit, 20 contracts are sampled at random. a)What is the probability that exactly four of them experience cost overruns? b)What is the probability that fewer than three of them experience cost overruns? c)Find the mean number that experience cost overruns. Round the answer to one decimal place. d)Find the standard deviation of the number that experience cost overruns.

Answer 1

n = 20

p = 0.12

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 4) = 20C4 * (0.12)^4 * (0.88)^16 = 0.1299

b) P(X < 3) = P(X =0) + P(X = 1) + P(X = 2)

                 = 20C0 * (0.12)^0 * (0.88)^20 + 20C1 * (0.12)^1 * (0.88)^19 + 20C2 * (0.12)^2 * (0.88)^18 = 0.5631

c) Mean = n * p = 20 * 0.12 = 2.4

d) Standard deviation = sqrt(np(1 - p)) = sqrt(20 * 0.12 * 0.88) = 1.45