Customers wanting to buy chocolate milk arrive at a convenie

Customers wanting to buy chocolate milk arrive at a convenience store according to a Poisson process with a rate of 2 per hour. The store is open from 8am until 4pm daily. You may assume that each customer wants to buy exactly 1 bottle of chocolate milk. In all parts of this problem, when I say “customers” I mean “customers that want to buy a bottle of chocolate milk.”

(a) What is the expected number of chocolate milk bottles that could be sold each day?
(b) What is the probability that no more than 2 customers show up between 2pm and 4pm, given that exactly 3 customers show up between 8am and 9am?
(c) What is the probability that the second customer will arrive within 15 minutes after the first customer arrived?

Need all a,b, and c

Solution