The question states: Let X = time between calls to a service center, It is known that X follows an exponential distribution with a mean of 15 minutes,

part 1. What is the probability that x is greater than 20 minutes?

So far this is the only one I think I've been able to work out. Since we know that the average is 15 i.e. μμ = 15, then λλ = 115115, which means that the probability of X > 20 is:

P(X>20) = e−λxe−λx = e−1e−1 or .3678 (36.78%)

the other questions are as follows:

part 2: if there are no service calls during the last 10 minutes what is the probability that there will be no service call during the next 30 minutes?

part 3: find the 90th percentile of X

part 4: what is the median time between calls to the service center.