Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$ 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 $=60\mathrm{.}75lb.$; Average range $\frac{?}{\text{b}\text{a}\text{r}}(R)=1\mathrm{.}64lb.$

a$)$ For the given sample size, the control limits for $3-$sigma $\stackrel{}{x}$ chart are:

Upper Control Limit $(UC{L}_{\stackrel{}{x}}^{-})=$

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

Lower Control Limit $(LC{L}_{\stackrel{}{x}})=$

Ib$.($round your response to three decimal places$).$

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

Upper Control Limit $(UC{L}_R)=$

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

Lower Control Limit $(LC{L}_R)=$

Ib$.($round your response to three decimal places$).$