Madan Lal & Sons is a fictional Indian manufacturer of highquality cricket balls.The balls are 100% handmade and consist of high-quality leather and other materials. To maintain its reputation as a high-quality producer, the company has strict quality control standards. The weight of a cricket ball has a huge impact on its quality. Typically, a ball weighs between 156 grams and 163 grams. Every day the company weighs a sample of five balls produced that day and records their weights. The following table shows the weights of the balls sampled during a 20-day period:

1. Design a mean and a range chart for the cricket-ball production process using 3σ control limits.

2. For the month of May, the company recorded the following 10 sample means and sample ranges.

Sample means: 158.3, 164.0, 158.3, 159.0, 161.5, 157.8, 160.3, 155.9, 163.1, and 158.6.

Sample ranges: 4.1, 6.3, 5.4, 5.9, 6.1, 6.4, 6.6, 6.7, 6.9, and 7.0.

Was the process in control during the month of May?

3. How would increasing the sample size from five to 20 affect the control chart? Would it change your conclusion in part b?

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Sample Weight (in grams) Sample Weight (in grams) 155.3, 156.0, 160.1, 154.9, 158.7 11 154.9, 155.8, 160.7, 155.9, 158.1 156.3, 157.0, 158.1, 159.9, 162.7 155.0, 156.9, 162.1, 159.9, 157.7 12 164.3, 162.8, 158.1, 156.4, 157.7 3 161.3, 159.0, 158.6, 164.2, 160.5 13 4 165.3, 164.0, 160.9, 161.9, 159.7 14 158.3, 157.4, 162.4, 163.1, 156.4 165.3, 159.4, 159.1, 162.5, 163.5 160.0, 158.0, 164.1, 158.9, 157.7 15 155.8, 157.5, 159.1, 157.9, 160.3 16 161.3, 159.1, 161.1, 153.9, 154.9 7 158.4, 153.0, 157.1, 158.2, 156.5 17 156.7, 162.0, 154.1, 157.9, 166.7 8. 160.0, 155.5, 162.7, 161.5, 156.2 18 159.3, 164.5, 162.8, 156.3, 158.0 9. 157.8, 159.0, 163.3, 158.9, 156.7 19 165.3, 159.5, 162.8, 157.9, 163.7 158. 0, 156 7, 160 8, 1579, 160,3 1657, 162.9, 156 1, 159 9, 163 7 10 20 5.