3. [Chapter 6S: 25 points] A production manager at Green Dishwashing Company is monitoring the quality of the company's production process. There has been concern relative to the quality of the operation in the accuracy of filling the 160 ounces of dishwashing liquid. Table 3. Sample (subgroups) Observations 1 2 3 4 5 6 7 8 9 10 1 164.0 159.7 159.1 162.0 158.7 154.3 164.3 155.0 161.3 156.8 2 161.1 161.0 160.0 162.1 162.1 154.9 162.1 159.2 162.1 164.3 3 159.0 162.0 160.4 159.3 163.4 155.5 159.9 161.2 160.5 162.0 4 157.8 158.1 159.2 159.5 164.3 159.2 160.0 160.2 160.1 159.7 1.1. Calculate the average values, x, and the range values, R, for each sample. Calculate the overall average, , and the average range, R. 1.2. Set up three-sigma control limits for average and range. Plot the data on the control charts (i.e., x-bar-chart and R-chart) and determine whether (1) the mean, (2) the range, and (3) the process distribution for samples 1-10 appear to be in control. Why? 1.3. Suppose the population standard deviation is known to be 2.50 ounces. Calculate three-sigma lower and upper control limits for average. Does your conclusion in (b) change? Why? 1.4. The product is designed for a fill of 160.003.0. The company collected the following sample data on the production process. Do you think the process is capable of meeting the design standard given a process standard deviation of 2.50 ounces?