The Good Chocolate Company makes a variety of chocolate candies, including a 12-ounce chocolate bar (340 grams) and a box of six 1-ounce chocolate bars (170 grams). A. Specifications for the 12-once

A. The largest standard deviation that the machine that fills the 12-ounce chocolate bar molds can have and still be considered capable if the average fill is 340 grams can be calculated using the formula: SD = (USL - LSL) / 6 where SD is the standard deviation, USL is the upper specification limit (344 grams), LSL is the lower specification limit (336 grams), and 6 represents the number of standard deviations between the upper and lower limits that cover 99.73% of the distribution. Plugging in the values, we get: SD = (344 - 336) / 6 = 1.33 grams Therefore, the largest standard deviation the machine that fills the 12-ounce chocolate bar molds can have and still be considered capable if the average fill is 340 grams is 1.33 grams. B. To determine if the process of filling the 1-ounce chocolate bar molds is capable, we need to calculate the process capability index (Cpk) using the formula: Cpk = min [(USL - mean) / 3?, (mean - LSL) / 3?] where USL is the upper specification limit (177 grams), LSL is the lower specification limit (163 grams), mean is the average fill (170 grams), ? is the standard deviation (0.76 gram), and 3 represents the number of standard deviations between the upper and lower limits that cover 99.73% of the distribution. Plugging in the values, we get: Cpk = min [(177 - 170) / (3 x 0.76), (170 - 163) / (3 x 0.76)] = min [0.96, 0.96] = 0.96 Since the Cpk value is greater than 1, the process is considered capable, and the filling machine is delivering chocolate bars within the specifications of the six-bar box. C. To provide capability in terms of the six-bar box, the filling machine should be set to deliver an average of 1 ounce per bar, which is equivalent to 28.3 grams. This is because the specifications for the six-bar box are 163 to 177 grams, and there are six 1-ounce bars in the box (6 x 28.3 grams = 169.8 grams). Therefore, an average fill of 28.3 grams per bar will ensure that the box is within the specifications.