Twenty-five consecutive samples of size n = 5 were collected to construct an x@chart. The sample means and ranges for the data are shown in the table. Sample xQ R Sample xQ R 1 80.2 7.2 14 83.1 10.2 2 79.1 9.0 15 79.6 7.8 3 83.2 4.7 1680.0 6.1 481.0 5.6 1783.2 8.4 577.6 10.1 1875.9 9.9 6 81.7 8.6 19 78.1 6.0 7 80.4 4.4 20 81.4 7.4 8 77.5 6.2 21 81.7 10.4 9 79.8 7.9 22 80.9 9.1 10 85.3 7.1 23 78.4 7.3 11 77.7 9.8 24 79.6 8.0 12 82.3 10.7 25 81.6 7.6 13 79.5 9.2

a. Calculate the mean of the sample means, x, and the mean of the sample ranges, R.

b. Calculate and plot the centerline and the upper and lower control limits for the x@chart.

c. Calculate and plot the A, B, and C zone boundaries of the x@chart.

d. Plot the 25 sample means on the x@chart and use the six pattern-analysis rules to determine whether the process is under statistical control.