The time in minutes between arrivals of customers to a post

The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.33. Please give your answers to two decimal places.

What is the probability that the time between consecutive customers is less than 15 seconds?

Solution

Given X follows Exponential distribution with mean=0.33

F(x)=1-exp(-0.33x) for x>0

So the probability that the time between consecutive customers is less than 15 seconds is

P(X<15) = 1-exp(-0.33*15) =0.99