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2. (20 points) The SC Department of Transportation Executive Director wants to explore the feasibility of tolls on I-26 to pay for redesigning and building Columbia's malfunction junction. On average, cars would arrive at a rate of 2000 per hour, Poisson distributed. Because toll booths would install card readers, regular SC drivers could get an EZ Pass that would charge them without having to stop and pay. Non-local drivers would have to wait at a toll booth to pay, but we aren't going to deal with that scenario in this problem. Drivers with an EZ Pass would have to slow down to go through the toll booth reader, which could charge at a rate of up to 2400 drivers per hour. Unfortunately, drivers will get backed up using this system as they have to choose a lane and wait behind the car in front of them. = and = (4 points) a. If there were just one EZ Pay toll booth scanner, what is the average time in the system that cars would have to spend in the entire system, waiting and being served, on average? Note: If you do this correctly, it will be a short time span that you should measure in seconds. Please convert to the time span that makes the most sense. ( 3 points) b. If there were just one toll booth, how many cars would be in the system, on average, at any point in time? (3 points) c. Recalculate the values in part (a) considering 2 and 3 toll booths in which cars would split themselves into separate lines. ( 6 points)