SOLUTION: The duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. If one class is randomly selected and the probability that the durati

Algebra ->  Probability-and-statistics -> SOLUTION: The duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. If one class is randomly selected and the probability that the durati      Log On


   

Question 1202234: The duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. If one class is randomly selected and the probability that the duration of the class is longer than a certain number of minutes is 0.536, then find the duration of the randomly selected class, i.e., if P(x>c)=0.536, then find c, where is c the duration of the randomly selected class. Round your answer to one decimal places.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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The duration of a professor's class has continuous uniform distribution
between 49.2 minutes and 55.5 minutes. If one class is randomly selected
and the probability that the duration of the class is longer than
a certain number of minutes is 0.536, then find the duration of the randomly
selected class, i.e., if P(x>c)=0.536, then find c, where is c the duration
of the randomly selected class. Round your answer to one decimal highlight%28cross%28places%29%29 place.
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In this problem with uniform distribution function,  the probability  P(x > c)  is

    P(x > c) = %2855.5-c%29%2F%2855.5+-+49.2%29 = %2855.5-c%29%2F6.3.


    +-----------------------------------------------------------------+
    |     It is a basic equation for the uniform distribution         |
    |   and knowing this equation is a pre-requisite, so I assume     |
    | that this equation is FAMILIAR to you and I should not explain  |
    |                         its origin.                             |
    +-----------------------------------------------------------------+


Thus they want you find the value of "c" from this equation

    %2855.5-c%29%2F6.3 = 0.536.    (1)


There is nothing easier than that. You need multiply both sides of the equation (1) by 6.3

    55.5-c = 0.536*6.3 = 3.3768


and simplify it further

    55.5 - 3.3768 = c

    c = 52.1232.


ANSWER.  c = 52.1  minutes  (rounded to one decimal place).

Solved.

Please write me if you do understand everything in my solution.