(a) Establish control chart limits for X bar and R charts with the following data. Calculate the process capability and interpret the meaning of control chart. [7] Measurements Sample 3 5 13 1 2 3 12 18 15 11 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 12 15 13 10 13 15 15 15 22 16 16 15 17 16 17 19 16 16 2 12 17 18 12 16 12 16 17 17 15 18 16 15 15 19 17 19 16 16 14 11 14 13 15 16 15 17 16 17 16 18 17 15 16 17 15 17 14 10 15 15 16 14 17 15 16 17 15 19 15 15 15 16 11 15 12 14 18 16 14 16 16 17 17 14 18 12 14 18 16 8 9 10 11 12 13 14 15 16 17 18 19 20 21 15 22 16 16 15 17 16 17 19 16 16 17 19 14 17 17 15 18 16 15 15 19 17 19 15 13 18 17 16 15 17 16 17 16 18 17 15 16 17 17 17 16 17 15 16 17 15 19 15 15 15 16 15 15 14 14 16 16 17 17 14 18 14 16 13 (b) A company that makes soft drinks wants to monitor the sugar content of its drinks. The sugar content (X) is normally distributed, but the means and variances are unknown. The target sugar level for one of its drinks is 15 grams. The lower spec limit is 10 grams. The upper spec limit is 20 grams.The company wants to know how much sugar on average is being put into this soft drink and how much variability there is in the sugar content in each bottle. The company also wants to know if the mean sugar content is on target. Lastly, the company wants to know t percentage of drinks that are too sweet and the percentage that are not sweet enough. To obtain this information, the company decides to sample 3 bottles of the soft drink at 3 different time each day: 10 A.M, 1:00 P.M. and 4:00 P.M. The company will use this data to construct an X-bar and R chart. Is it right methodology to take decision? Why? Plot X-bar and R chart. [3]