A manufacturer of digital quartz watches claims that 5% of its watches run for more than

1-minute fast or slow after a year of use. A consumer protection agency has purchased

twelve of the manufacturer’s watches with the intention of testing the claim

(a) If the manufacturer’s claim is correct, what is the probability that eight of thewatches are accurate within a minute?(b) If the manufacturer’s claim is correct, what is the probability that at least 10 of thetwelve watches are accurate within a minute?(c) If the manufacturer’s claim is correct, what is the probability that anywhere from8 to 11 of the twelve watches are accurate within a minute?