Customers arrive at restaurant according to a Poisson distribution at the rate of 20 per hour. The restaurant opens for business at 11:00 a.m. Find the following:

(a) The probability of having 20 customers in the restaurant at 11:12 a.m. given that there were 18 at 11:07 a.m.

(b) The probability a new customer will arrive between 11:28 and 11:30 a.m. given that the last customer arrived at 11:25 a.m.

Books previously ordered arrive at a university library according to a Poisson distribution at the rate of 25 books per day. Each shelf in the stacks can hold 100 books. Determine the following:

(a) The expected number of shelves that will be stacked with new books each month.

(b)The probability that more than 10 books cases will be needed each month given that a book case has five shelves.