Periodically, the Federal Trade Commission (FTC)

monitors the pricing accuracy of electronic checkout scanners at stores to ensure consumers are charged the correct price at checkout. A 1998 study of over 100,000 items found that one of every 30 items is priced incorrectly by the scanners (Price Check !I: A Follow-Up Report on the Accuracy of Checkout Scanner Prices, Dec. 16,1998). Suppose the FTC randomly selects five items at a retail store and checks the accuracy of the scanner pricc of each. Let x represent the number of the five items that is priced incorrectly.

a. Show that x is (approximately) a binomial random variable.

b. Use the information in the FTC study to estimate p for the binomial experiment.

c. What is the probability that exactly one of the five items is priced incorrectly by the scanner?

d. What is the probability that at least one of the five items is priced incorrectly by the scanner?