A machine is used to fill cans of soup with a nominal volume of 0.450 litres. Suppose that the machine delivers a quantity of soup which is normally distributed with mean a litres and standard deviation o litres. Given that = 0.457 and a 0.004, find the probability that a randomly chosen can will contain less than the nominal volume. It is required by law that no more than 1% of cans contain less than the nominal volume. Find

(a) the least value of which will comply with the law if er 0.004,

(b) the greatest value of o which will comply with the law if -0.457. (MEI)