Jam is packed into tins of advertised weight 1 kg The weight of a randomly selected tin of jam is normally distributed about a target weight with al standard deviation of 12 g.

(a) If the target weight is 1 kg, find the probability that a randomly chosen tin weighs (i) less than 985 g. (ii) between 970 g and 1015 g.

(b) If not more than one tin in 100 is to weigh less than the advertised weight, find the minimum target weight required to meet this condition.

(c) The target weight is fixed at 1 kg. The resulting tins are packed in boxes of six and the weight of the box is normally distributed with mean weight 250 g and standard deviation 10 g. Find the probability that a randomly chosen box of 6 tins will weigh less than 6.2 kg. (L)