# 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.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.8320$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.8376$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.8435$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8532$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.8692$

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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.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 15.11$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 15.43$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 15.75$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 16.25$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 16.78$

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