# Exam C Practice Problem 21 – Working with Aggregate Claims

Problem 21-A

You are given the following:

• The annual number of claims follows a Poisson distribution with mean 800.
• The claim size follows a Gamma distribution with $\alpha$ = 5 and $\theta$ = 2.
• The number of claims and the claim sizes are independent.

Using the normal approximation for the distribution of aggregate claim costs, calculate the probability that the aggregate claim costs will exceed 8350? $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.11$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.13$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.15$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.17$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.20$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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Problem 21-B

You are given the following:

• The annual number of claims follows a geometric distribution with mean 8.
• The claim size follows an exponential distribution with mean 5.
• The number of claims and the claim sizes are independent.

Using the normal approximation for the distribution of aggregate claim costs, calculate the 75th percentile of aggregate claim costs? $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 64$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 66$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 68$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 70$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 75$

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___________________________________________________________________________________ $\copyright \ 2013 \ \ \text{Dan Ma}$