A chocolate manufacturer makes a variety of chocolate products including large chocolate bars (340 grams) and boxes of six smaller chocolate bars (170 grams in total).
a. Specification for a large bar is 330 grams to 350 grams. What is the largest standard deviation (in grams) that the machine that fills the bar moulds can have and still be considered capable if its average fill is 340 grams?
b. The machine that fills the bar moulds for the smaller bars has a standard deviation of .80 grams. The filling machine is set to deliver an average of 28.5 grams per bar. Specification for the 6-bar box is 160 to 180 grams. Is the process capable? Hint: The variance of the box’s weight is equal to six times the variance of each smaller bar’s weight.
c. What is the lowest setting (in grams) for the smaller-bar filling machine that will leave the process for the 6-bar box capable?