Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$ for this problem.

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 recorded:

For the given$$ data, the x double overbar $=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $3$

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

Upper Control Limit $($UCL Subscript x overbar$)=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $4$

Lower Control Limit $($LCL Subscript x overbar$)=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $5$

Based on the x overbar$-$chart, is one or more samples beyond the control$$ limits$?$

$$

Yes

No

$.$

Part $6$

For the given$$ data, the Upper R overbar $=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $7$

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

Part $8$

Upper Control Limit $($UCL Subscript Upper R$)=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $9$

Lower Control Limit $($LCL Subscript Upper R$)=$

$$

enter your response here inches $($round your response to four decimal$$ places$).$

Part $10$

Based on the$$ R$-$chart, is one or more samples beyond the control$$ limits$?$

$$

No

Yes

$.$