Response to the following problem:
The California Highway Patrol conducts random truck inspections on certain California highways. On a particular day, three Highway Patrol units have set up an inspection station for checking truck brakes. Whenever one of the three units become available, the next trucker to pass the inspection point is pulled over for inspection. When all three units are busy, no other trucks are stopped until a unit becomes free. Trucks travel down the highway according to a Poisson process. On the average, one truck approaches the inspection station every 50 seconds. The time required to inspect brakes averages five minutes and has a standard deviation of 1.5 minutes.
a. What proportion of trucks on the highway will be inspected?
b. What is the probability that all three Highway Patrol units are idle?
c. On the average, how many trucks will be having their brakes inspected?