The Merrimack Airlines company runs a commuter air service between Manchester, New Hampshire, and Cape Cod, Massachusetts. Since the company is a small one, there is no set schedule for their flights, and no reservation is needed for the flights. However, it has been determined that their planes arrive at the Manchester airport according to a Poisson process with an average rate of 2 planes per hour. Vanessa arrived at the Manchester airport and had to wait to catch the next flight.
a. What is the mean time between the instant Vanessa arrived at the airport until the time the next plane arrived?
b. What is the mean time between the arrival time of the last plane that took off from the Manchester airport before Vanessa arrived and the arrival time of the plane that she boarded?