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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 place.
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In this problem with uniform distribution function, the probability P(x > c) is
P(x > c) = = .
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| 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. |
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Thus they want you find the value of "c" from this equation
= 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.