The time interval T, in minutes, between patient arrivals in an emergency room is a random variable

with exponential density function p(t) = 0:125e^-.125t. What is the average time between patient
arrivals? What is the probability of two patients arriving within 3 min of each other?

For average wait time,
I believe it is 8 minutes because if you look at the function the mean is r, which based on the equation would be 8 (is this right?)

For probability of two average within 3 minutes of each other
I took the integral of 0 to 3 of the function and got -e^-t/8 from 0 to 3, which I calculated to be .3217 (does this sound right?)

Thanks!