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A general contracting firm experiences cost overruns on
Chapter 4, Problem 8E(choose chapter or problem)
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 exactly four of them experience cost overruns?
b. What is the probability that fewer than three of them experience cost overruns?
c. What is the probability that none of them experience cost overruns?
d. Find the mean number that experience cost overruns.
e. Find the standard deviation of the number that experience cost overruns.
Questions & Answers
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 exactly four of them experience cost overruns?
b. What is the probability that fewer than three of them experience cost overruns?
c. What is the probability that none of them experience cost overruns?
d. Find the mean number that experience cost overruns.
e. Find the standard deviation of the number that experience cost overruns.
ANSWER:Step 1 of 6
Given, that in a sample of 20 contracts, general contracting cost overruns on 20% of its contracts.
Let X follow a binomial distribution with probability mass function is
\(\mathrm{P}(\mathrm{x}: \mathrm{n}, \mathrm{p})=\left(\begin{array}{l} n \\ x \end{array}\right) p^{x}(1-\mathrm{p})^{(n-x)}, \mathrm{x}=0,1,2, \ldots \ldots, \mathrm{n}\)
Where,
n = sample size
= 20
x = random variable
p = probability of success
= 20%
= 0.20
q = 1 - p (probability of failure)
The mean of the binomial distribution is
\(\mu_{x}=n p\)
Variance of the binomial distribution is
\(\sigma_{x}^{2}=\mathrm{npq}\)