Planes enter the queue to take off at an airport with a sing

Planes enter the queue to take off at an airport with a single takeoff runway at a rate of 2 per 5-minute period. If the time taken by each plane to dear the runway is exponentially distributed with average time 1.5 minutes, calculate the average number of planes in the queue waiting to take off; (ii) the average time a plane has to wait in the queue to take off; the probability that 2 or more planes are waiting in the queue to take off.

Solution

Ans: Given the data, there are 2 planes that enter the queue in every 5 minutes.

The tim etaken by each plane to clear the runway is exponentially distributed with an average of 1.5minutes.

Here = no. of planes arriving there per hour. As there are 2 planes every 5 minutes, each hour there are 24 planes.

Then = No of planes clearing off in an hour= 60/1.5= 40