4-16. An insurance company reviews insurance claims received for payment, and re

Question

4-16. An insurance company reviews insurance claims received for payment, and rejects 40% of the claims. The insurance claims follow a Poisson process with a rate = 200 claims per year. What is the probability that a claim will be rejected? What is the mean and standard deviation of the number of claims per year? What is the mean and standard deviation of the number of rejected claims per year assuming independence among claim rejection? What is the probability of rejecting more than 100 claims per year?

Explanation / Answer

probability that a claim will be rejected =0.4

mean of the number of claims per year = =200

standard deviation of the number of claims per year =()1/2=(200)1/2 =14.1421

mean of the number of rejected claims per year assuming independence among claim rejection=np=200*0.4=80

standard deviation of the number of rejected claims per year assuming independence among claim rejection

=(np(1-p))1/2 =(200*0.4*(1-0.4))1/2 =6.9282

probability of rejecting more than 100 claims per year =P(X>100)=1-P(X<=100)=1-P(Z<(100.5-80)/6.9282)

=1-P(Z<2.9589) =1-0.9985 =0.0015

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