Customers make purchases at a convenience store, on average, every six minutes. It is fair to assume that the time between customer purchases is exponentially distributed.

Jack operates the cash register at this store.

a. What is the rate parameter? What is the standard deviation of this distribution?

b. Jack wants to take a five-minute break. He believes that if he goes right after he has serviced a customer, he will lower the probability of someone showing up during his five-minute break. Is he right in this belief?

c. What is the probability that a customer will show up in less than five minutes?

d. What is the probability that nobody shows up for over half an hour?