A particular brand of sugar is sold in bags labelled 1kg. The actual weights are approximately normally distributed with a mean of 1004g and a standard deviation of 2.9g.
(a) What is the probability of a customer being sold an underweight (less than 1kg) bag of sugar?
(b) (i) Find the Z score corresponding to the bottom 4% of the N(0,1) distribution.
(ii) Assuming the filling variability achievable by the packaging machine cannot be improved, what would the mean bag weight need to be to ensure that no more than 4% of customers are sold an underweight bag?