Natural Foods sells Takeoff, a breakfast cereal, in one-pound boxes. According to Food and Drug Administration (FDA) regulations, a one- pound box must contain at least 15.5 ounces of cereal. However, Natural Food’s box- filling process is not perfect: its precision, expressed in terms of the standard deviation of the weight of a one- pound box filled, is 0.5 ounces.
a. Where should Natural Foods center its process in order to ensure that 98% of boxes filled meet FDA requirements? What proportion of boxes would be overfilled beyond 16 ounces?

b. While underweight boxes might prompt FDA action, overweight boxes certainly cost Natural Foods in terms of higher material costs. Therefore, quality control manager Morris Nerdstat wants to monitor the cereal- filling process in order to ensure that its mean does not deviate from the level established in Part a. He plans to weigh nine randomly selected boxes at regular time intervals and plot the average weight on a chart. At one point, he finds an average weight of 15.9 ounces. The company’s legal staff is pleased that this performance is better than the FDA requirement of 15.5 ounces. What action, if any, should Nerdstat take? 

c. What targets (in terms of the mean and the standard deviation) would result in the process with six- sigma capability?