I need help with the following problem 4:

Problem 3. Store management (20 pts) A store has customers walking in at an average rate of 5 customers per hour. One in 4 customers coming to the store are new customers, the others are returning customers. We model the customer arrivals with a Poisson process. The store is open from 8am to 8pm. (a) Find the probability that at least 8 customers arrive by 9am ? (b) If 8 customers arrive by 9am, what is the probability that exactly two of them are new customers ? (c) Find the probability that no returning customer will arrive within 30 min of the rst new customer ? (d) The store had 64 customers visit during a given day. What is the probability that none of them came after 6 pm ? (e) We assume that a new customer spends according to an Exponential distribution with average $20 and a returning customer spends according to an Exponential distribution with average $10. Determine the average amount of sales in the store on any given day. Problem 4. Arrival Times (10 pts) We consider a Poisson process (Ngo with parameter A. We assume that at some time T, 71 events have happened (i.e. NT = n). What are the expected time of arrival of the rst and of the last event ? Application: In the store described in Problem 3, on a given day, 71 customers arrived to the store. Give an approximate time at which the rst and the last customer arrived