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    Density Functions: Time takes students to finish aptitude test

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    1. The time it takes for a student to finish an aptitude test has the density function
    f(x) = c(x-1) (2-x), 1<x<2
    = 0, otherwise.
    Here the unit of time is an hour.
    a) Evaluate the Normalizing constant c.
    b) Plot the density function
    c) Calculate the probability that a student will finish the test in less than 75 minutes
    d) Calculate the probability that a student will finish the test between 1.5 and 2 hours.
    e) Make some comments about the plot of the density function.

    2. For the density f(x) = 375/(x^4), for x>5 and zero otherwise.
    a) Find the median
    b) Find the 90th percentile
    c) Find the 10th percentile

    3. Let f(x) be the uniform density on [0,1] and let g(x) be the density on [0,1] given by g(x)=ce^x, where c is the normalizing constant. Let F, and G be the corresponding CDFs. Find the density function corresponding to the new CDF H(x) = F(x)G(x).

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    https://brainmass.com/statistics/probability-density-function/density-functions-time-takes-students-finish-aptitude-test-388731

    Solution Preview

    1. The time it takes for a student to finish an aptitude test has the density function
    f(x) = c(x-1) (2-x), 1<x<2
    = 0, otherwise.
    Here the unit of time is an hour.
    a) Evaluate the Normalizing constant c.
    b) Plot the density function
    c) Calculate the probability that a student will finish the test in less than 75 minutes
    d) Calculate the probability that a student will finish the test between 1.5 and 2 hours.
    e) Make some comments about the plot of the density function.
    Solution
    a) Since is a probability density function we have

    That is,
    That is,
    That is,
    That is,
    That is,
    That is,
    That is,
    That is,
    Therefore, ...

    Solution Summary

    The expert determines the time it takes for students to finish aptitude tests.

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