A what would the upper and lower control limits be

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a. What would the upper and lower control limits be for the resulting control charts  (average and range)? b. Five samples of voltage are taken with the following results: Sample 1 2 3 4 5 x-bar 3.6 3.3 2.6 3.9 3.4 R 2.0 2.6 0.7 2.1 2.3 What action should be taken, if any? c. Discuss the pros and cons of using this variables control chart versus the control chart  described in problem 4.  Which do you prefer and why? 8. A machining operation requires close tolerances on a certain part for automobile engines.  The  current tolerance for this measurement is 3.0 cm +/- .001.  The quality control procedure is to take 
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a sample of size 4 and measure each of the parts.  On the basis of past samples of size 4, x-bar-bar  = 3.0 and R-bar = .0015. a. Construct an average and range chart for this part. b. On the basis of the following data, is the process in control? Sample 1 2 3 4 5 x-bar 3.0005 2.9904 3.0010 3.0015 3.0008 R 0.0024 0.0031 0.0010 0.0040 0.0010 c. Is the process running outside of its tolerances? 9. A bank has noticed an apparent recent decline in the daily demand deposits.  The average daily  demand deposit balance has been running at $106 million with an average range of $10 million  over the past year.  The demand deposits for the past six days have been 110, 102, 96, 87, 115, and  106.   a. What are the CL, UCL, and LCL for the x-bar and R charts based on a sample size of 6? b. Compute an average and range for the past six days.  Do the figures for the past six days  suggest a change in the average or range from the past year? 10. A grocery store purchases fresh fish every day from its supplier.  It has ordered 100 pounds of fish  each day, but the weight actually received varies from day to day with an average range of 4  pounds.  Over the past five days it received the following weights of fish: 106, 94, 102, 100, and  97 pounds. a. Using this five-day sample is the process of the fish supplier in control in average and  range? b. How can the supplier more carefully control the process to provide nearly 100 pounds of  fish each day?
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