5. Arrivals at a rural entrance booth to the New York State Thruway are considered to be Poisson distributed with a mean arrival rate of 20 vehicles per hour. The time to process an arrival is...

5. Arrivals at a rural entrance booth to the New York State Thruway are considered to be Poisson distributed with a mean arrival rate of 20 vehicles per hour. The time to process an arrival is approximately exponentially distributed with a mean time of one min.

i) What percentage of the time is the tollbooth operator free to work on operational reports?

ii) How many cars are expected to be waiting to be processed, on average, per hour?

iii) What is the average time a driver waits in line before paying the toll?

iv) Whenever the average number of waiting vehicles reaches 5, a second tollbooth will be opened. How much will the average hourly rate of arrivals have to increase to require the addition of a second operator?