A manufacturer of a new Smart Watch claims that the probability of its watch running more than 1 minute slow or 1 minute fast after 1 year of use is .05. A consumer protection agencyhas purchased four of the manufacturer's watches with the intention of testing the claim.

a. Assuming that the manufacturer's claim is correct, what is the probability that none of the watches are as accurate as claimed?

b. Assuming that the manufacturer's claim is correct, what is the probability that exactly two of the four watches are as accurate as claimed?

c. Suppose that only one of the four tested watches is as accurate as claimed. What inference can be made about the manufacturer's claim? Explain.

d. Suppose that none of the watches tested are as accurate as claimed. Is it necessarily true that the manufacturer's claim is false? Explain.