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 resultswere:

Sample

Sample Mean(in.)

Range (in.)

Sample

Sample Mean (in.)

Range (in.)

1

14.10414.104

0.0330.033

7

14.10114.101

0.0410.041

2

14.10014.100

0.0410.041

8

14.10314.103

0.0340.034

3

14.09114.091

0.0340.034

9

14.09514.095

0.0270.027

4

14.10814.108

0.0510.051

10

14.10314.103

0.0290.029

5

14.09514.095

0.0310.031

11

14.10314.103

0.0390.039

6

14.09914.099

0.0360.036

12

14.10614.106

0.0470.047

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

Based on the sampling done, the control limits for 3-sigma x overbar chart are:
Upper Control Limit (UCL Subscript x overbar) = inches(round your response to four decimal places).
Lower Control Limit (LCL Subscript x overbar) = inches(round your response to four decimal places).
Based on the x overbar-chart, is one or more samples beyond the control limits? YES Or NO?
.
For the given data, the Upper R overbar = (round your response to four decimal places).
The control limits for the 3-sigma R-chart are:

Upper Control Limit (UCL Subscript Upper R) = inches(round your response to four decimal places).

Lower Control Limit (LCL Subscript Upper R) = 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?