A hostel in Country X can have 20 guests in capacity and offer guests a choice of a full English breakfast, a continental breakfast, or no breakfast. The probabilities of the choices being made are 0.45, 0.25 and 0.3 respectively. It is assumed that the breakfast choice is independent among guests. (a) On a particular morning, there are full houses in the hostel. Calculate the probability that (i) at least 3 guests prefer a continental breakfast, (ii) more than 4 and at most 6 guests prefer a full English breakfast. (b) Calculate the mean and the standard deviation for the number of guests requiring breakfast when there are 18 guests in the hostel.

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