In 1996, the Bureau of Consumer Protection of the Federal Trade Commission (FTC) conducted a study to investigate the accuracy of electronic checkout scanners. They inspected the pricing accuracy of scanners on 17,928 items in 294 department, discount, drug, food, and other retail stores, and discovered that 4.82% of the items scanned for amounts that differed from the advertised or posted price. Let’s assume that 4.82% represents the true error rate.
a. Briefly explain why the binomial probability model is appropriate for the counts of miss-canned items in a random selection of scanned items.
b. Find the probability that in the next 1000 randomly selected items that are scanned for purchase, exactly 15 are scanned incorrectly for price.
c. Is it reasonable to use the Poisson model to approximate the probability found in Part B?
d. Regardless of your answer to Part C, use the Poisson probability to find the approximate probability that exactly 15 are scanned incorrectly for price. Is the Poisson approximation close to the exact binomial probability?