Question: (15 points) The local roads commission has asked for your help in determining how badly traffic will be delayed if a local road must be closed for short periods of time while it is being resurfaced. Cars arrive at random times during the day at a particular point on the road, with an arrival rate of 6 per hour. If the workers close the road immediately after a car passes, what is the probability that only 2 cars have arrived at the end of the next 30 minutes?

a) (1pt) Define the random variable for this problem.
b) (6 pts) Explain exactly how the random variable defines above is distributed.
c) (2 pts) Write out the probability question for this problem.
d) (6 pts) What is the probability that only 2 cars have arrived at the end of the next 30 minutes?