A company recently developed a new valve. Each valve is required to be between 4.50 and 5.50 inches long with a target value of 4.90 inches. The company collected 10 samples of 50 valves each to assess the quality of their new production process. The following table shows the average length of the valve (in inches) for each sample and the mean and standard deviation of those averages. 1. Is the process in control using a z of 3? [Note: You do not need to provide a control chart here; just compute upper and lower control limits and compare to sample means to answer that question.] 2. What is the sigma-capability and the process capability index of this process? 3. Is the mean of the process correctly located? 4. The company is targeting a 3-sigma process. Using only your answers to the previous parts, answer the following questions: Does the company have a 3-sigma process? If not, is the issue location of the mean or variability or both? [Note: For determining the location of the mean, compare the mean from the given sample and the target value of the length of the valve that is specified in the question]