a$)$ Determine the upper and lower control limits and the overall means for x overbar$-$charts and$$ R$-$charts.

For the given$$ data, the x double overbarequals

$$

$8\mathrm{.}4005$ cm$.($Enter your response rounded to four decimal$$ places.$)$

Part $3$

For the given$$ data, the Upper R overbarequals

$$

$0\mathrm{.}0369$ cm$.($Enter your response rounded to four decimal$$ places.$)$

Part $4$

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

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

$$

$8\mathrm{.}4218$ cm$.($Enter your response rounded to four decimal$$ places.$)$

Part $5$

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

$$

$8\mathrm{.}3792$ cm$.($Enter your response rounded to four decimal$$ places.$)$

Part $6$

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

Part $7$

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

$$

$0\mathrm{.}0780$ cm$.($Enter your response rounded to four decimal$$ places.$)$

Part $8$

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

$$

enter your response here cm$.($Enter your response rounded to four decimal$$ places.$)$