In the past few years, outsourcing overseas has become more frequently used than ever before by European companies, especially in the area of customer services. 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.

a. What is the probability that exactly fi ve companies that outsource overseas use a consultant?

b. What is the probability that more than nine companies that outsource overseas use a consultant?

c. What is the probability that none of the companies that outsource overseas use a consultant?

d. What is the probability that between four and seven (inclusive) companies that outsource overseas use a consultant?

e. Construct a graph for this binomial distribution. In light of the graph and the expected value, explain why the probability results from parts

(a) to

(d) were obtained.