The weight of cement in a medium-size bag is stated to be 10 kilograms. The amount that the packaging machine puts in these bags is believed to have a Normal model with a mean of 10.2 kilograms and a standard deviation of 0.12 kilograms.

a) What fraction of all bags sold are underweight?

b) Some of the cement is sold in “bargain packs” of three bags. What’s the probability that none of the three is underweight?

c) What’s the probability that the mean weight of the three bags is below the stated amount?

d) What’s the probability that the mean weight of a 24-bag case of cement is below 10 kilograms?