Please answer the following questions in Q&A format

1. In 200-300 words. What is a control chart? What are the grand mean, the UCL, and the LCL of a control chart for the mean? Why do you suppose ±3 standard errors are used in control charts and not two or even one standard error? Explain 2.Respond to the following statement in minimum 75 words: A control chart is a graphing tool used in statistics to study effects of how a process evolves or changes over time. A control chart can also commonly be referred to as statistical process control. The data that is used for the control chart is graphed in specific order, ranging in order of time. When looking at a control chart, the average is displayed in the form of a central line; aside from the control chart displaying the average on the graph, the upper limit and lower limit are also displayed by means of an upper line and a lower line. The terms used when describing the upper limit and lower limit on a control chart is the UCL for upper control limit and LCL for lower control limit. When calculating the control limits for the control chart, they are done by estimating the standard deviation, sigma of the sample data. Once that is complete, the next step is to multiply the number/result by three (3) and once that is complete the last step is to add (3xsigma to the average which will give the UCL, then subtract (3xsigma from the average) which will give the LCL. The reason that +-3 standard errors are used in control charts rather than two or one standard error is because is it is combination that relates closest to the lowest sum of alpha beta plus decision errors. Black, K. (2017) Business Statistics for Contemporary Decision Making (9th Edition) Hoboken, NJ: John Wiley & Sons, Inc. 3.Respond to the following statement minimum 75 words: The purpose of a control chart would be to track the progress of a study over time. The process changes are plotted in order of time. The control chart has three distinct lines, the central line that is the average, the upper control line, and the lower control limit. The three lines represent historical data. The current data is compared to the historical data in order to show the conclusion of the process. If the information is consistent, then the researcher can determine that the graph is in control, but if the information is unpredictable, the results would be that it is variable or out of control. Control charts are used in several scenarios. One of the uses of this type of table would be to view an ongoing process to find and correct a problem that continues to occur. Other reasons for the graph would be to look to see if a process is stable or if the company is expecting a different range of outcomes. The chart can help a company determine if a quality improvement could prevent specific problems or plan to make changes in a plan. Many employees continue to use the same methods for a project because that is how it has always been done but is that the best way or should the process change to create a better outcome. 4. In 200-300 words Explain regression analysis and identify why it is important for business managers to understand this type of statistic. How is regression analysis applicable in day to day business operations. 5. Summarize all of the above. Provide citation and reference to the material(s) you discuss. Describe what you found interesting regarding this topic, and why. Describe how you will apply that learning in your daily life, including your work life. Describe what may be unclear to you, and what you would like to learn. 6. Respond to the following in minimum 75 words: I had a significant experience yesterday when i sat down to start the calculations needed in our individual assignment this week. My impending sense of doom that I have had the last five weeks was not there. I took each data set individually and calculated what the assignment required and when i recognized interesting patterns I made additional correlations for my narrative. The value in this confidence is immediately transferable to my professional role. Rather than being intimidated by the process, I have learned skills to drill deeper than the original metric needed. My interface with excel functions has improved and I appreciate the confidence to create control charts and report on variations in a way that I can describe the implications in different ways based on my audience. I am still struggling with how I would prove anything in a sampling when I do not have access to the population, but probability is a comforting and significantly reliable tool moving forward in professional forecasting.