An insurance company is issuing 16 car insurance policies.Suppose the probability for a claim during a year is 15 percent.If the binomial probability distribution is applicable,then the probability that there will be at least two claims during the year is equal to

Question

Quizplus · Accepted Answer

If p is the probability of a claim during a year and n is the number of policies, then the number of policies with a claim follows a binomial distribution with parameters n and p.

Thus, the probability that there will be at least two claims during the year is given by the complement of the probabilities that there will be 0 or 1 claim:

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)

= 1 - (0.85)^16 - 16(0.15)(0.85)^15

= 0.7161

Therefore, the answer is C.

An Insurance Company Is Issuing 16 Car Insurance Policies