Full Question: If a shop receives orders at an average rate of 4 per hour and receives an order at 10am, what time will there be a 75% chance that at least one additional order has been received since 10am?
I'm really confused on how to get started.I know that an order is supposed to come in every 15 minutes. My only idea is to do a poisson approximation but i know its not right.
My Attempt:
.75=[(e^x)*(x^.75)]/.75!
Hint: If $\ T_n\ $ is the length of time between the arrival of the $\ n$-th and $\ n+1$-th orders, then $\ T_n\ $ has an exponential distribution with a mean of $\ 15\ $ minutes.