All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 120 per eight-hour day (Poisson distributed), and the station can weigh, on the average, 140 trucks per day (Poisson distributed). Suppose arriving truck drivers look to see how many trucks are waiting to be weighed at the weigh station. If they see four or more trucks in line, they will pass by the station and risk being caught and ticketed.
What is the probability that a truck will pass by the station?
Here’s the way to look at this, in terms of an 8 hour day. Do not convert measures to minutes. So we have:
Arrival rate of trucks = 120 / day
Service rate = 140 / day
If 4 trucks are waiting while one is being serviced, the total number of trucks in the system = 5.
So find the probably of more than 5 trucks using the complement rule P(X>5) = 1- P(X<=5)