A machine filling 18-gram containers of a hair dye is set so that the average fill is 18.2 grams with a variance of 0.49 grams. Assume that the filling of containers by this machine is normally distributed.
(a) What percentage of the containers is not likely to meet the producer's specification of at least 18 grams per container?
(b) What is the minimum mass of the heaviest 15% of containers?
Note: Calculate the results for (a) and (b) using the z-table and then the appropriate Excel function (i.e. NORMDIST or NORMINV).