International Data Corp. (IDC) has shown that the average return on business analytics projects was almost four-and-a-half times the initial investment.

Analytics consists of tools and applications that present better metrics to the user and to the probable future outcome of an event. IDC looked at how long it takes a typical company to recoup its investment in analytics.

It determined that 29% of the U.S. corporations that adopted analytics took six months or less to recoup their investment. The file entitled Analytics contains a sample of the time it might have taken 35 corporations to recoup their investment in analytics.

a. Determine the number of corporations that recovered their investment in analytics in six months or less.

b. Calculate the probability of obtaining at most the number of corporations that you determined in part a if the percent of those recovering their investment is as indicated by IDC.

c. Determine the 70th percentile of the number of the 35 corporations that recovered their investment in analytics in six months or less. (Hint: Recall and use the definition of percentiles from Section 3.1.)