A machine dispenses peanuts into bags so that the weight of peanuts in a bag is normally distributed.

(a) Initially the mean weight of peanuts in a bag is 128.5 g and the standard deviation is 1.5 g. Find the probability that the weight of peanuts in a randomly chosen bag exceeds 130g-

(b) The machine is given a minor overhaul that changes the mean weight, p, of peanuts in a bag without affecting the standard deviation. Following the overhaul, 14% of bags contain more than 130 g of peanuts. Find, to four significant figures, the new value for .

(c) Later the machine requires a major repair, following which the mean weight of peanuts in a bag is 128.3 g, and 4% of bags contain less than 126 g. Find, to three significant figures, the standard deviation of the weight. of peanuts in a bag after this major repair. (NEAB)