# Exam P Practice Problem 101 – auto collision claims

Problem 101-A

The amount paid on an auto collision claim by an insurance company follows a distribution with the following density function. $\displaystyle f(x) = \left\{ \begin{array}{ll} \displaystyle \frac{1}{96} \ x^3 \ e^{-x/2} &\ \ \ \ \ \ x > 0 \\ \text{ } & \text{ } \\ \displaystyle 0 &\ \ \ \ \ \ \text{otherwise} \\ \end{array} \right.$

The insurance company paid 64 claims in a certain month. Determine the approximate probability that the average amount paid is between 7.36 and 8.84. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.8320$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.8376$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.8435$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8532$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.8692$ $\text{ }$ $\text{ }$ $\text{ }$

Problem 101-B

The amount paid on an auto collision claim by an insurance company follows a distribution with the following density function. $\displaystyle f(x) = \left\{ \begin{array}{ll} \displaystyle \frac{1}{1536} \ x^3 \ e^{-x/4} &\ \ \ \ \ \ x > 0 \\ \text{ } & \text{ } \\ \displaystyle 0 &\ \ \ \ \ \ \text{otherwise} \\ \end{array} \right.$

The insurance company paid 36 claims in a certain month. Determine the approximate 25th percentile for the average claims paid in that month. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 15.11$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 15.43$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 15.75$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 16.25$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 16.78$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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