4. A water vending machine at the local supermarket is designed to fill 20-litre water bottles. Every 5 hours, a sample of 5 water bottles is taken and the contents of the bottles are carefully measured. While the filling process was in control, the average of the sample means was found to be 19.85 L and the average of the sample range was found to be 0.3 L. (15 Marks) a. Calculate 30 control limits for mean and range charts to monitor this process. Mean = 19.85 L Range = 0.3 L Sample size n = 5 value A2 = 0.577 Mean UCL = 19.85 + 0.577 x 0.3 = 20.02 LCL = 19.85 - 0.577 x 0.3 = 19.68 Centerline 19.85 Range UCL R x D4 = 0.3 x 2.114 = 0.63 LCL R x D3 = 0.3 x 0 = 0 Centre line of R Chart - mean 0.03