An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company
Question:
An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company representative claims that 80% or more of policy holders have smoke detectors. You draw a random sample of 8 policy holders.
a. If exactly 80% of the policy holders have smoke detectors
(so the representative’s claim is true, but just barely), what is the probability that at most 2 of the 8 sampled policy holders have smoke detectors?
b. Based on the answer to part (a), if 80% of the policy holders have smoke detectors, would 2 policy holders with smoke detectors in a sample of size 8 be an unusually small number?
c. If you found that 2 of the 8 sample policy holders had a smoke detector, would this be convincing evidence that the claim is false? Explain.
d. If exactly 80% of the policy holders have smoke detectors, what is the probability that at most 6 of the 8 sampled policy holders have smoke detectors?
e. Based on the answer to part (d), if 80% of the policy holders have smoke detectors, would 6 policy holders with smoke detectors in a sample of size 8 be an unusually small number?
f. If you found that 6 of the 8 sample policy holders had smoke detectors, would this be convincing evidence that the claim is false? Explain.
Step by Step Answer: