A machine is used for filling paper bags with flour. The machine allows the target weight of flour per bag to be adjusted. Long historical records show that the distribution of the weight of flour released is normal with mean equal to the target value and a standard deviation of 0.01 kg.
(a) If the target weight is set to 1.01 kg of flour what proportion of bags will have less than 1 kg of flour?
(b) Determine the target weight that will ensure that only 1% of bags will be under 1kg.
(c) A machine salesman claims that a new computer operated filling machine is much more accurate and can therefore save money in the long run. Suppose that you wish to retain the rule that only 1% of bags contain less than 1 kg of flour. You also calculate that the targeted weight would need to be set at 1.005 kg to justify the extra cost of the new filling machine. What would the standard deviation of the new filling machine have to be in order to satisfy these criteria?