Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem being:

Sample Size, n	Mean Factor, A2	Upper Range, D4	Lower Range, D3
2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284

Twelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanual Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were:

Sample Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 9.904 0.044 7 9.903 0.021 2 9.904 0.051 8 9.903 0.058 3 9.893 0.042 9 9.893 0.039 4 9.904 0.037 10 9.901 0.038 5 9.899 0.048 11 9.903 0.054 6 9.899 0.053 12 9.904 0.061

For the given data, the x = ______inches (round your response to four decimal places).

Based on the sampling done, the control limits for the 3-sigma x chart are:

Upper Control Limit (UCLx) = ______inches (round your response to four decimal places).

Lower Control Limit (LCLx) = _______inches (round your response to four decimal places).

Based on the x-chart, is one or more samples beyond the control limits? Yes or No

For the given data, the R = _______ inches (round your response to four decimal places).

The control limits for the 3-sigma R-chart are:

Upper Control Limit (UCLR) = ______inches (round your response to four decimal places).

Lower Control Limit (LCLR) = ______ inches (round your response to four decimal places).

Based on the R-chart, is one or more samples beyond the control limits? Yes or No