Permit x be the number of policyholder who make at least one claim to a large insurance company. Suppose that there are 2000 policyholders and that each one has probability 0.2 of making at least one claim throughout the year. Compute the probability that no more than 500 policyholders will make claims throughout any given year?
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This task provides a clear description of the use of continuity correction. The given problem is a binomial probability problem and since the sample size (n = 2000 > 30) is very large, we apply the continuity correction and the binomial distribution tends to normal distribution. This approximation is valid only when both np and nq is greater than 5.