Question 1 [26 marks] A production manager wants to control the gap width between the positive and negative electrodes of a battery to ensure the quality of the product. Twelve (m = 12) samples of n = 10 observations have been obtained, and the sample means and ranges in millimetres (mm) of gap widths are recorded as shown in the table below. Sample 1 2 34 5 6 7 8 9 10 11 12 Sample Mean 4.93 5.23 4.97 5.02 5.11 5.02 5.22 5.15 5.01 4.92 5.24 5.15 Sample Range 0.70 0.55 0.59 0.75 0.69 0.27 0.56 0.90 0.49 0.56 0.41 0.65 1. What type(s) of control chart should be used for controlling the gap width between the positive and negative electrodes? Why? [4 marks] 2. Construct control charts based on three-sigma limits. What conclusion can you draw based on the control charts? Provide your explanations. [12 marks] 3. If the specification range for the gap width of two electrodes is between 4.90mm and 5.10mm, is the process capable of meeting the specification? Justify your answer. [10 marks]