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-ounce bar are 326 grams to 354 grams. What is the largest standard deviation (in grams) that the machine that fills the bar molds can have and still be considered capable if the average fill is 340 grams? (Round your intermediate calculations to 2 decimal places and final answer to 3 decimal places.) St

Answer:A) ≈ 3.509 grams B) The process is not capable because the lowest Cpk which is 1.89 ≈ 1.9 is far from the ideal 1.33 capability index number ( NO )c) 1.051 ouncesExplanation:A) The largest standard deviation ( in grams) This can be calculated applying the capability index formula and according to the capability index formula the value at which a process is capable is at  : 1.33hence the largest standard deviation =  upper limit - lower limit / 6 * 1.33  ( 354 - 326 ) / 7.98 = 3.5087 ≈ 3.509 grams B) we first calculate the process mean and std of the box standard deviation = [tex]\sqrt{variance }[/tex]std of the six-bar box = [tex]\sqrt{6*0.86^2}[/tex]  = 2.106process mean = 6 * ( 1.03 * 28.33) = 175.079the mean is not centered between the upper specification and the lower specification hence we will apply the formulae used in calculating the capability index for an uncentered processCpk = (upper value - process mean) / (3 * std of box),          = (187 - 175.079) / ( 3 * 2.106) = 11.921 / 6.318 = 1.89Cpk =  (process mean -  lower value ) / (3*std of box)        = ( 175.079 - 153 ) / (3 * 2.106) = 22.079 / 6.318 = 3.49The process is not capable because the lowest Cpk which is 1.89 ≈ 1.9 is far from the ideal 1.33 capability index number ( N0 )c ) lowest setting calculate the value of the mean using capability index of 1.33 Cpk = (upper value - mean ) / 3 * std mean = 187 - 1.33 * 3 * 2.106            = 187 - 8.40 = 178.60 grams Cpk = ( process mean - lower value ) / 3 * std  mean = 1.33 * 3 * 2.106 + 153             = 8.40 + 153 = 161.40 grams the lowest setting in ounces = 178.60 / ( 6 bar * 28 .33) = 178.60 / 169.98 = 1.051 ounces