Suppose an audit process is taking place at a small airport, and the head auditor arrives randomly throughout the day and assesses the operation of the airport. She shows up in one-hr intervals at a time. The time between aircraft arrivals at this small airport is exponentially distributed with a mean of 75 minutes. You may assume the operation of the small airport is independent of the time interval under consideration.

What is the amount of time (in hours) such that the probability of aircraft arrivals in the interval is 75%?

What is the probability that the third interval the auditor shows up for is the second interval with at least four aircraft arrivals?

If the auditor decides to show up four different times in a day, what is the mean of the number of intervals she will experience with less than four aircraft arrivals?