# Exam P Practice Problem 49 – Aggregate Claim Costs

Problem 49-A

The aggregate claim amount (in millions) in a year for a block of fire insurance policies is modeled by a random variable $Y=e^X$ where $X$ has a normal distribution with mean 4 and variance 2. What is the expected annual aggregate claim amount?

$\displaystyle (A) \ \ \ \ \ \ \ 403.43$

$\displaystyle (B) \ \ \ \ \ \ \ 244.69$

$\displaystyle (C) \ \ \ \ \ \ \ 148.41$

$\displaystyle (D) \ \ \ \ \ \ \ 90.02$

$\displaystyle (E) \ \ \ \ \ \ \ 54.60$

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Problem 49-B

The aggregate claim amount (in millions) in a year for a block of fire insurance policies is modeled by a random variable $Y=e^X$ where $X$ has a normal distribution with mean 1.15 and variance 1.2. What is the probability that the annual aggregate claim amount will be less than the expected annual aggregate claim amount?

$\displaystyle (A) \ \ \ \ \ \ \ 0.5000$

$\displaystyle (B) \ \ \ \ \ \ \ 0.6915$

$\displaystyle (C) \ \ \ \ \ \ \ 0.7088$

$\displaystyle (D) \ \ \ \ \ \ \ 0.8749$

$\displaystyle (E) \ \ \ \ \ \ \ 0.9599$

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