A hotel has a total of 300 identical rooms. It has an overbooking policy to maximize the usage of its available capacity. Assume that each potential customer holding a room reservation, independently of other customers, cancels the reservation or simply does not show up at the hotel on a given day with probability 0.15. (You can use R in your computations but be sure that you show your work)

(a) Find the largest number of room reservations that the hotel can book and still be at least 95% sure that everyone who shows up at the hotel will have a room on a given night.

(b) Given that the hotel books a total of 320 reservations, find the probability that at most 90% of the available rooms will be oc- cupied on a given night.