Question: VERCOR provides merger and acquisition consultants to assist corporations when owners decide to offer their business for sale. One of its news releases, "Tax Audit Frequency Is Rising," written by David L. Perkins Jr., a VERCOR partner, and which originally appeared in The Business Owner, indicated that the proportion of the largest businesses, those corporations with assets of $10 million and over, that were audited was 0.17.
a. One member of VERCOR's board of directors is on the board of directors of four other large corporations. Calculate the expected number of these five corporations that should get audited, assuming selection is random.
b. Three of the five corporations were actually audited. Determine the probability that at least three of the five corporations would be audited if 17% of large corporations are audited. (Assume random selection.)
c. The board member is concerned that the corporations have been singled out to be audited by the Internal Revenue Service (IRS). Respond to these thoughts using probability and statistical logic.