One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample, x has a _______________.
A)normal distribution
B)hypergeometric distribution, but may be approximated by a binomial
C)binomial distribution, but may be approximated by a normal
D)binomial distribution, but may be approximated by a Poisson
E)exponential distribution

Question

Quizplus · Accepted Answer

The situation described is a classic example of a hypergeometric distribution because we have a finite population (100 claims) from which a sample is drawn without replacement, and we are interested in the number of successes (fraudulent claims) in the sample. However, when the sample size is small relative to the population, the hypergeometric distribution can be approximated by a binomial distribution.

One Hundred Policyholders File Claims with CareFree Insurance