3. Commercial trucks traveling through Monument, Colorado must stop at a weigh station. Trucks arrive at the station at an average rate of 16 per hour (Poisson distributed), and it takes on average of 2.8 minutes to weigh each truck (following an exponential distribution) on the single scale. a. What is the average number of trucks waiting to be weighed? b. How long, on average, does a truck spend at the weigh station (including the time in line, and the time being weighed)? c. The weigh station can operate safely with up to 8 trucks in the system. What is the probability that this capacity will be exceeded? d. A national trucking association estimates that the cost of an idle truck is $39 per hour. In an 8 hour day, what does the weigh station cost the trucking industry? e. Adding another person to work at the weigh station would cost $22 per hour, and would allow trucks to be processed in 2.4 minutes. Should the trucking industry offer to pay for this additional worker? Hint: For parts d and e, note that a truck is essentially "idle" during the entire