**A busy railway station has two taxi stands at separate exits, A. At stand A, taxis arrive according to a Poisson Process of rate 2 per minute.
Following the arrival of a train, a queue of 40 customers suddenly builds up at stand A, waiting for taxis to arrive. Assume that whenever a taxi arrives, it instantly picks up exactly one customer (if there is one), and assume that all customers in the queue patiently wait their turn. Approximately calculate the probability that the 40th customer in the queue has to wait longer than 15 minutes in total before boarding a taxi.**
Not quite sure which distribution this question is hinting at. My first thought was that it was the normal distribution but the question doesn't hint at a standard deviation, so that I can put into the equation.
Second thought was that it could be the poison distribution but that's about finding the probability of the number of times an event happens in a fixed time interval.