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 $=57\mathrm{.}75lb.$; 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 $(UC{L}_{\frac{?}{\text{b}\text{a}\text{r}}()})=$

lb$.($round your r

Lower Control Limit $(LC{L}_{\frac{?}{\text{b}\text{a}\text{r}}()})=$

lb$.($round your re

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

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

lb$.($round your n

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

Ib$.($round your $r$

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