SOLUTION: A continuous random variable has a uniform distribution. Find the probability of the given event. Suppose the reaction time x (in minutes) of a certain chemical process follows

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Question 1183805: A continuous random variable has a uniform distribution. Find the probability of the given event.
Suppose the reaction time x (in minutes) of a certain chemical process follows a uniform probability distribution with 5≤x≤15 . Find the probability that the given reaction time is greater than 8 min.

Answer by ikleyn(52776) About Me  (Show Source):
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A continuous random variable has a uniform distribution. Find the probability of the given event.
Suppose the reaction time x (in minutes) of a certain chemical process follows a uniform
probability distribution with 5≤x≤15 . Find the probability that the given reaction time
is greater than 8 min.
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Yesterday  I  solved a  TWIN  problem at this link

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1183790.html

https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1183790.html

So,  this time I will be short.


    P = %2815-8%29%2F%2815-5%29 = 7%2F10 = 0.7 = 70%.    ANSWER

As always in such problems,  you divide the  "favorable"  time interval length by the base interval length.

It is how the uniform distribution probability works.


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Comment from student :   Thank you for your help! I  checked the link and I noticed that problem was  "less than"
while this one is "greater than).  So for either way, they are solved the same?


My response :   You are right.  The major idea is the same

        P = favorable_time_interval%2Fbase_time+interval.


The only thing is to take care to calculate the numerator and denominator correctly.