2 A hotel has 50 single rooms, 16 of which are on the ground floor. The hotel offers guests a choice of a full English breakfast, a continental breakfast or no breakfast. The probabilities of these choices being made are \(0.45,0.25\) and 0.30 respectively. It may be assumed that the choice of breakfast is independent from guest to guest.

1. On a particular morning there are 16 guests, each occupying a single room on the ground floor. Calculate the probability that exactly 5 of these guests require a full English breakfast.
2. On a particular morning when there are 50 guests, each occupying a single room, determine the probability that:
   1. at most 12 of these guests require a continental breakfast;
   2. more than 10 but fewer than 20 of these guests require no breakfast.
3. When there are 40 guests, each occupying a single room, calculate the mean and the standard deviation for the number of these guests requiring breakfast.