Problem XXXXXXXXXXpoints) The manufacturer of a price-reading optical scanner claims that the probability it will misread the price of any product by misreading the bar code on a product’s label is...

Problem 3. (20 points) The manufacturer of a price-reading optical scanner claims that the probability it will misread the price of any product by misreading the bar code on a product’s label is 0.001. When such a scanner was installed in a supermarket, the store manager tested its performance. Let Y be the number of trials (i.e., the number of bar codes read by the scanner) until the first misread price is observed. a) Assuming that the manufacturer's claim is correct, find the probability distribution for Y (assume that the trials are independent events) b) Assuming that the manufacturer's claim is correct, what is the probability that the scanner will not misread a price until after the fifth bar code is read? c) If the store manager observes that the third bar code is misread, what inference would you make about the manufacturer's claim? Explain.