Monto sherry is sold in bottles of two sizes: standard and large. For each size, the content, in litres, of a randomly chosen bottle is normally distributed with mean and standard deviation as given in the table. Standard Mean deviation Standard bottle Large bottle 0.760 0.008 1.010 0.009

(a) Show that the probability that a randomly chosen standard bottle contains less than 0.750 litres is 0.1056, correct to four places of decimals.

(b) Find the probability that a box of 10 randomly chosen standard bottles contains at least 3 bottles whose contents are cach less than 0.750 litres. Give three significant figures in your answer.

(c) Find the probability that there is more sherry in 4 randomly chosen standard bottles than in 3 randomly chosen large bottles. (C)