Monthly Archives: March, 2016

Exam P Practice Problem 95 – Measuring Dispersion

Problem 95-A

The lifetime (in years) of a machine for a manufacturing plant is modeled by the random variable X. The following is the density function of X.

    \displaystyle  f(x) = \left\{ \begin{array}{ll}           \displaystyle  \frac{3}{2500} \ (100x-20x^2+ x^3) &\ \ \ \ \ \ 0<x<10 \\            \text{ } & \text{ } \\           0 &\ \ \ \ \ \ \text{otherwise}           \end{array} \right.

Calculate the standard deviation of the lifetime of such a machine.

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.0

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.7

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3.0

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4.0

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4.9

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Problem 95-B

The travel time to work (in minutes) for an office worker has the following density function.

    \displaystyle  f(x) = \left\{ \begin{array}{ll}           \displaystyle  \frac{3}{1000} \ (50-5x+\frac{1}{8} \ x^2) &\ \ \ \ \ \ 0<x<20 \\            \text{ } & \text{ } \\           0 &\ \ \ \ \ \ \text{otherwise}           \end{array} \right.

Calculate the variance of the travel time to work for this office worker.

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3.87

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5.00

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6.50

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8.75

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 15.00

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\copyright \ 2016 \ \ \text{Dan Ma}