2. (30 pts) A juice manufacture thinks its filling machines might be getting old. Historically their average juice is 8 oz/ bottle with a range of 1 oz. The company takes several samples of 10 juices each and observes the following data (Note: if z is needed, let z = 3). Please provide two decimal points for your UCL and LCL. a) Draw a control chart for the mean. b) Draw a control chart for the range. c) Do you think the juice filling process is (more likely) in control or not? Historical Sample 1 2 3 4 5 6 7 benchmark Average 8 8.0 9.0 8.0 7.0 11.0 6.0 13.0 (oz) Range (oz) 1 0.9 0.7 0.9 1.1 1.2 1.3 1.3 Question 3 (40 points) In the busy bank (Q2), Washington Mutual bank is considering opening more drive-thru windows to increase capacity. Recall, in this busy location, customers arrive at an average of 1 every 2 minutes and each teller can still serve 20 customers an hour. Assume Poisson arrival times and Exponential service times. a) What is the optimal number of windows if they would like the probability of a customer waiting in a line to be less than 10%? What will the probability a customer will wait at your chosen staffing level? b) What is the optimal number of windows if each teller is paid $25 per hour and the bank has a marketing ploy that if anyone who waits more than 6 minutes will get $6.