Provide support for your response by citing from the readings or other scholarly

Provide support for your response by citing from the readings or other scholarly writings.
1. Compare and contrast the rational subgroup sampling method with the random sampling method that is often used in scientific research. Why is rational subgroup preferred for process behavior charts? 2. Explain the rationale for the use of plus and minus three standard deviations from the centerline for the control limits. Why was this selected as the standard for process behavior charts? 3. For average and sigma control charts, the standard deviation, or s, is computed for each subgroup using the subgroup average rather than the grand average. Provide a proof of the difference between s calculated from a subgroup and s calculated from a grand average. Discuss the difference. 4. Provide some real-world examples for the appropriate use of median and moving range charts. Why are these types of behavior charts still in use today when most businesses have access to computers? 5. Discuss the questions each type of control chart answers and compare them, i.e., averages, ranges, p, np, c, and u.