The process of painting the body-work of a (C) mass-produced lorry consists of giving it one coat of paint A, three coats of paint B and two coats of paint C. A record of the quantity of each type of paint used for each coat is kept for each lorry produced over a long period. The following table gives the means and standard deviations of these quantities measured in litres: Standard Mean deviation The coat of paint A 3.7 0.42 Each coat of paint B 1.3 0.15 Each coat of paint C 1.0 0.12 Assuming independence of the distribution for each coat, calculate the mean and standard. deviation for the total quantity of paint used on each lorry. Assuming that the quantities of paint used for each coat are normally distributed, calculate

(a) the percentage of lorries receiving less than 8.5 litres of paint,

(b) the percentage of lorries receiving more than 10.0 litres of paint. (C)