(b) A hotel has 50 single rooms, 16 of which are on the ground floor. The hotel offers guests a choice of a cooked break

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(b) A hotel has 50 single rooms, 16 of which are on the ground
floor. The hotel offers guests a choice of a cooked breakfast,
continental breakfast or no breakfast. The probabilities of the
choice 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.
i. 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 cooked breakfast.
ii. On a particular morning when there are 50 guests, each
occupying a single room, determine the probability that,
(a) at most 12 of these guests require a continental
breakfast
(b) more than 10 but fewer than 20 of these guests require no
breakfast.
iii. When there are 40 guests, each occupying a single room,
calculate
(a) the mean and for the number of these guests requiring
breakfast.
(b) the standard deviation for the number of these guests
requiring breakfast.