The mass of grapes sold per day in a (C) supermarket can be modelled by a normal distribution. It is found that, over a long period, the mean mass sold per day is 35.0 kg, and that, on average, less than 15.0 kg are sold on one day in twenty.

(a) Show that the standard deviation of the mass of grapes sold per day is 12.2 kg. correct to three significant figures.

(b) Calculate the probability that, on a day chosen at random, more than 53.0 kg are sold.

(c) Ten days are chosen at random. Assuming independence, find the probability that less than 15.0 kg will be sold on exactly two of these days. (C)