Question 2: Value = 25 points

A small commuter airport has a single runway and one air traffic controller to land planes. It takes an airplane an average of 8 minutes to land and clear the runway (exponentially distributed). Planes arrive at the airport every 10 minutes on average. Assume that departing planes do not interfere with the landing operations and answer the following questions:

1. Determine the average number of planes that will stack up waiting to land. (5 pts)

2. Find the average time a plane must wait in line before it can land. (5 pts)

3. Calculate the average time it takes from the moment a plane has notified the airport that it is in the vicinity and wants to land until the plane has cleared the runway. (5 pts)

4. Find the probability that there are more than two planes stacked up waiting to land. (5 pts)

5. If a second air traffic controller is hired, identify the average number of planes waiting to land and the average time a plane must wait in line from the computer printout given below. (There are several columns; part of your job is to identify the correct column to us. (5 pts)