I am unsure when to use integer correction. My study manual says to use integer correction if you are trying to find P[n<X<m] and X is discrete and integer valued.

So I thought that integer correction should be used on the following problem:

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

I did this problem using integer correction because I thought that it was supposed to be used.

Can someone explain why it should not be used in this case?

In what cases should integer correction be used?

Thanks a lot!

So I thought that integer correction should be used on the following problem:

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

I did this problem using integer correction because I thought that it was supposed to be used.

Can someone explain why it should not be used in this case?

In what cases should integer correction be used?

Thanks a lot!

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