A production manager wants to control the gap width between thepositive and negative electrodes of a battery to ensure the qualityof the product. Twelve (m = 12) samples of n = 10 observations havebeen obtained, and the sample means and ranges in millimetres (mm)of gap widths are recorded as shown in the table below.
| Sample | 1 | 2 | 3 | 4 | 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 forcontrolling the gap width between the positive and negativeelectrodes? Why? mean chart or range chart or both? reasons?
2. With three-sigma control limits, what conclusion can you drawbased on the control charts? Provide your
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