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 $=57\mathrm{.}75lb$; Average range $\frac{?}{\text{b}\text{a}\text{r}}(R)=1\mathrm{.}54lb.$

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

Upper Control Limit $(UC{L}_{\stackrel{}{x}})=,$ Ib$.($round your response to three decimal places$).$

Definition

$\backslash$table$[[\backslash$table$[[$Sample$],[$Size$,n$

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

Upper control limit $($UCLvR$)=$

Lower control limit $($LCLvR$)=$