Truck s are required to check in a weigh station (seal e) so that they c an be inspected for weight violations. Trucks arrive at the station at the rate of 40 an hour in the mornings according to Poisson distribution. Currently two inspectors are on duty' during those hours, each of whom can inspect 25 trucks an hour, according to Poisson distribution.
a. How many trucks would you expect to see at the weigh station, including those being inspected?
b. If a truck were just arriving at the station, how many minutes could the driver expect to wait before being inspected?
c. How many minutes, on average, would a truck that is not immediately inspected have to wait before being inspected?
d. What is the probability that both inspectors would be busy at the same time (i.e., the probability that an arrival will have to wait for service)?
e. What condition would exist if there were only one inspector?
f. If only 13 trucks fit in the system, what is the probability that a truck cannot enter the system?