If three customers are checked out per minute at a store wha

If three customers are checked out per minute at a store, what is the chance, with you being the third in line, that it takes 5 minutes or more to be checked out? (distribution question)

Solution

let X be the random variable representing the time to check out

X follows exponential distribution with parameter a = 1/3

cumulative distribution function of exponential distribution is

P(X>x) = e^(-ax)

=>

P(X>5) = e^(-5/3) = 0.1889