1. (13 marks] Every hour a random sample of 10 bottles of milk tea is selected from the output to monitor the filling process. Here are data on 8 such samples. Measurements are in millilitre (ml). 1 2 3 4 5 6 7 8 Sample Sample Mean 270.8 Sample Range 14.8 269.4 271.3 272.5 8.4 18.6 270.7 13.8 264.5 9.1 269.3 12.2 271.5 9.7 Average 270.0 12.0 9.4 You are required to draw control charts to evaluate the process. What conclusion can you draw about the process and the control limits? 1 2 3 5 6 7 8 Figure 2: Control chart of Question AQ2. 1 2 3 5 6 7 8 Figure 3: Control chart of Question AQ2. 2. (5 marks) Assume that the filling process is quite standardized and is thought to be highly stable, with a mean of 271 ml. It has been specified that the bottled milk tea should fall between 260 ml and 280 ml. What is the largest standard deviation (in ml) that the process can have in order to guarantee that this process is capable of meeting the specification