The weight of potato chips in a medium-size bag is stated to be 300g. The amount that the packaging machine puts in the bags is believed to have a normal distribution with mean 306g and standard deviation 3.6g.
a) What fraction of all bags sold are underweight?
b) Some of the chips are sold in bargain packs of three bags. What is the probability that none of the three bags in underweight?
c) What is the probability that the mean weight of the three bags is below the stated weight?
d) What is the probability that the mean weight per bag of a 24-bag case of potato chips in below 300g?