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Part $1$

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

$$Thirty$-$five samples of size $7$ each were taken from a$$ fertilizer$-$bag$-$filling machine at Panos Kouvelis Lifelong Lawn Ltd$.$ The results$$ were: Overall mean$=57\mathrm{.}75$lb$.$; Average range Upper R overbar $=1\mathrm{.}54$ lb$.$

$$a$)$ For the given sample$$ size, the control limits for $3-$sigma x overbar chart $$are:

Part $2$

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

$$

enter your response here lb$.($round your response to three decimal$$ places$).$

Part $3$

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

$$

enter your response here lb$.($round your response to three decimal$$ places$).$

Part $4$

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

Part $5$

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

$$

enter your response here lb$.($round your response to three decimal$$ places$).$

Part $6$

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

$$

enter your response here lb$.($round your response to three decimal$$ places$).$