Soup is sold in tins which are filled by a machine. The actual weight of soup delivered to a tin by the filling machine is always normally distributed about the mean weight with a standard deviation of 8 g. The machine is set originally to deliver a mean weight of 810 g.

(a) Determine the probability that the weight of soup in a tin, selected at random, is less than 800 g-

(b) Determine the probability that the weight of soup in a tin, selected at random, is between 795 g and 820 g. Proposed legislation requires that not more than 2.5% of tins may contain less than the nominal net weight of 800 g.

(c) Assuming that the value of the standard deviation remains unchanged, determine the minimum mean weight that the machine should be set to deliver in order to comply with this requirement. (NEAB)