The manager of Avalon at the Prudential Center, a large apartment complex in Boston, collects the rent from each tenant on the first day of every month. Past records indicate that the mean number of tenants who do not pay the rent on time in any given month is 4.7. Consider the rent collection for the next month.

(a) Find the probability that every tenant will pay the rent on time.

(b) Find the probability that at least seven tenants will be late with their rent.

(c) Suppose the number of delinquent rent payments in a month is independent of the number in every other month. What is the probability that at most three tenants will be late with their rent in two consecutive months?

(d) State and explain any assumption you make to answer the above questions.