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

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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.

\text{ }

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

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

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

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

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

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Answers can be found in this page.

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Daniel Ma

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