Blueberry Boxes is a local company that grows and sells blueberries in boxes (what else were you expecting!). The company is using wooden boxes instead of plastic in order to reduce carbon footprint. Typical pack size of these is labeled 16 oz. which represents the net weight of blueberries in a box at the time of packing. The company has purchased a Chinese machine that fills berries in boxes. Their experience with such packaging machine shows that the fill is almost normally distributed with a standard deviation of 0.2 oz. The company understands that if they set the average at 16 then 50% of the boxes will be filled less than 16 oz. They think that will make many customers unhappy and are particularly concerned about underweight boxes. Someone suggested that they can set the machine to fill somewhat more than 16 oz and that should take care of the problem. After a lot of discussions, the management decided to set the average fill at 16.3 oz. while the label still claims 16 oz. a. What percentage of the packs will be filled less than 16 oz? b. The quality management team thinks that no more than 4% of packs should be less than 16 oz. If that is the goal what should be the mean setting at the machine? c. Blueberries cost $1.5 /lb to the company and the CEO is very upset with above decision. She thinks they will be giving away too much free product. She insists that the machine should be set back to 16.2 oz. mean fill and still have no more than 4% underweight boxes! Is she crazy or what? Is it possible? Can you think of a way to achieve this goal?