An insurance company offers a discount to home-owners who install smoke detectors in their homes. a company representative claims that 80% or more of policyholders have smoke detectors. you draw a random sample of eight policyholders. let x be the number of policyholders in the sample who have smoke detectors. a. if exactly 80% of the policyholders have smoke detectors ( so the representative's claim is true, but just barely), what is p( x ≤ 1)? b. based on the answer to part (a), if 80% of the policyholders have somke detectors, would one policyholder with a smoke detectors in a sample of size 8 be an unusually small number? c. if you found that exactly one of the eight sample policyholders had a smoke detector, would this be convincing evidence that the claim is false? explain d. if exactly 80% of the policyholders have smoke detectors, what is p(x≤ 6)? e. based on the answer to part (d), if 80% of the policyholders have smoke detectors, would six policyholders with smoke detectors in a sample of size 8 be an unusually small number? f. if you found that exactly six of the eight sample policyholders had smoke detectors, would this be convincing evidence that the claim is false? explain.