Suppose that, after a grocery store opens, people walk into the store at the rate of 3 per minute. Suppose each person stays in the grocery store for an exponentially distributed time with a mean of 20 minutes, and then leaves. Let X(t) be the number of people in the grocery store t minutes after the store opens. (a) Give the state space, birth rates, and death rates for the birth and death process (X(t), t 0). (b) What is the probability that, after the store opens, at least three people arrive before anyone leaves