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 different policyholders are mutually independent. Calculate the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

Step-by-step explanation:

The total number of claim is the sum S of 1250 independent random variables,

each having poisson distribution with mean μ = 2

Since the  Variance of poisson distribution is equal to its mean ,

the standard deviation of this is

By the CLT is follow that S is approximately normal with mean 1250*2 =2500

and standard deviation

Hence, the probability to compute is

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step-by-step explanation: