This pandemic, PCI Bank opens a drive-thru window for customers to complete bank transactions without getting out of their cars. Arrivals occur at random, with an arrival rate of 30 customers per hour.

a. What is the mean or expected number of customers that will arrive in a five- minute period? b. Assume that the Poisson probability distribution can be used to describe the arrival process. Compute: i. the probability that exactly 0 will arrive during a five-minute period ii. the probability that exactly 2 will arrive during a five-minute period c. Assume that the service times for the drive-thru window follow an exponential probability distribution with a service rate of 42 customers per hour. Use the exponential probability distribution to answer the following questions:

i. What is the probability the service time is one minute or less? ii. What is the probability the service time is two minutes or less?