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. $ \mu$ = 15, then $\lambda$ = $\frac{1}{15}$, which means that the probability of X > 20 is:
P(X>20) = $e^{-\lambda x}$ = $e^{-1}$ 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.
can anyone help me solve these problems?