R-Chart Control Limits

From a process known to be in control, 6 random samples of 5 units each were taken and weighed. The mean and range for each of the 6 samples are given in the following table.

Sample Mean Range

1 7.2 0.7

2 7.6 1.0

3 7.1 1.4

4 7.8 1.1

5 7.8 0.6

6 7.5 1.2

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a. Calculate the 3 X-chart and R-chart control limits.

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b. Calculate the mean (X) and range (R) for the following sample, which was taken from the same process at a later time.

Item number:12345

Weight:7.58.0 8.27.57.4

Based on this sample and the control chart limits that you calculated in part (a), is the process in control? Why or why not?