The number of vehicles crossing a line on an interstate is Poisson with an average of 5 per hour. A slug arrives at the interstate and | will wait until no vehicles have crossed the line for 5 minutes until it attempts to get to the other side of the interstate. (This particular slug can count and tell time.) Assume the cars are independent.
a. For a given 5-minute period, what is the expected number of cars to cross the line?
b. What is the probability that no vehicles will pass in a given 5-minute period?
c. How many 5-minute intervals will the slug have to wait until the first one with no vehicles?
d. It will take the slug 10 minutes to cross the road. What is the probability the slug will be run over by at least one car? (Start the clock and the car-counting when the slug starts crossing the road.)