Question

In the past few years, outsourcing overseas has become more frequently used than ever before by U.S. companies. However, outsourcing is not without problems. A recent survey by Purchasing indicates that 20% of the companies that outsource overseas use a consultant. Suppose 15 companies that outsource overseas are randomly selected. Based on the relevant binomial distribution, what is the probability that exactly five companies that outsource overseas use a consultant? [ Round your answer to 4 decimal places] Group of answer choices 0.1032 0.1101 0.9389 .2041

Answer 1

P(X=5)=0.1032

Explanation:

This variable can be modeled by a binomial distribution, with parameters n=15 (sample size) and p=0.2 (the individual probability that the company use a consultant).

The probability that k companies that outsource overseas use a consultant can be written as:

`P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\\\\\\P(x=k) = \dbinom{15}{k} 0.2^(k) 0.8^(15-k)\\\\\\`

Then, the probability that exactly five companies that outsource overseas use a consultant is:

`P(x=5) = \dbinom{15}{5} p^(5)(1-p)^(10)=3003*0.0003*0.1074=0.1032\\\\\\`