2. Vehicles arrive at a toll bridge at an average rate of 180 an hour. Only one toll booth is currently open and can process arrivals (collect tolls) at a mean rate of 22 seconds per vehicle.

A. How many vehicles should be expected at the toll bridge in a 10-minute period? Please show how you arrived at your answer.

B. Define X to be the number of vehicles arriving at the toll bridge in a 10-minute period and assume that X has a Poisson Probability distribution. Please calculate the probability that 25 vehicles will arrive at the toll bridge in a 10-minute period.

C. Please calculate the probability ofat least20 vehicles arriving at the bridge within 10-minute period.

D. Please calculate the probability ofless than28 vehicles arriving at the bridge within 10-minute period.

E. Please calculate the probability thatnovehicle will arrive at the bridge within a 10-minute period.

F. Please calculate the probability ofmore than35 vehicles arriving at the bridge within a 10-minute period. Show your work.

G. Please calculate the probability ofat most22 vehicles arriving at the bridge within a 10-minute period. Show your work.

G. Calculateandinterpretthe standard deviation of X.

I. For what purpose can the kind of information you have calculated above be used? If the state department of transportation wants to reduce the average wait time for the drivers to less than 25 seconds at the toll bridge, do you think they should open another toll booth at the bridge? Please explain.