Machine A, used for filling bags with ground coffee, can be set to dispense any required mean weight of coffee per bag. At any setting the weight of coffee in a bag can be modelled by a normal distribution with a standard deviation of 1.95 g.

(a) If the machine is set to dispense a mean weight of 128 g of coffee per bag, calculate the percentage of bags that contain less than 125 g.

(b) To meet an official regulation the setting on a machine must be adjusted so that no more than 1% of bags contain less than 125 g. (i) Calculate the smallest mean weight to which machine A should be set to meet the regulation. (ii) Machine B will only just meet the regulation when it is set to dispense a mean weight of 128.5 g. Assuming that the weight of coffee is a bag filled by Machine B can be modelled by a normal distribution, calculate the standard deviation of this distribution. (NEAB)