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

Thirty$-$five samples of size $10$ each were taken from a chocolate packaging machine at a confectionery called Sweet Delights to evaluate the weight of chocolate bags. The results were: Overall mean $=60\mathrm{.}75lb.$; Average range $\frac{?}{\text{b}\text{a}\text{r}}(R)=1\mathrm{.}78lb.$

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

Upper Control Limit $(UC{L}_{\frac{?}{\text{b}\text{a}\text{r}}()})=$ Ib$.($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 $(UC{L}_R)=$ Ib$.($round your response to three decimal places$).$

$$ Lower Control Limit $(LC{L}_R)=$ Ib$.($round your response to three decimal places$).$