Question 1202234
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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(cross(places))}}} <U>place</U>.
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<pre>
In this problem with uniform distribution function,  the probability  P(x > c)  is

    P(x > c) = {{{(55.5-c)/(55.5 - 49.2)}}} = {{{(55.5-c)/6.3}}}.


    +-----------------------------------------------------------------+
    |     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

    {{{(55.5-c)/6.3}}} = 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.


<U>ANSWER</U>.  c = 52.1  minutes  (rounded to one decimal place).
</pre>

Solved.


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