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Factors for calculating three$-$sigma limits for the $\backslash (\backslash$overline$\{\backslash$mathrm$\{$x$\}\}\backslash )-$chart and R$-$chart

$\backslash$begin$\{$tabular$\}\{$cccc$\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Size of $\backslash \backslash$

Sample $\backslash ((\backslash$mathbf$\{$n$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Factor for UCL and LCL $\backslash \backslash$

for $\backslash (\backslash$overline$\{\backslash$mathbf$\{$x$\}\}\backslash )-$chart $\backslash (\backslash$left$(\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{2\}\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Factor for LCL $\backslash \backslash$

for R$-$Chart $\backslash (\backslash$left$(\backslash$mathbf$\{$D$\}\_\{\backslash$mathbf$\{3\}\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Factor for UCL $\backslash \backslash$

for R$-$Chart $\backslash (\backslash$left$(\backslash$mathbf$\{$D$\}\_\{\backslash$mathbf$\{4\}\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $2$ & $1\mathrm{.}880$ & $0$ & $3\mathrm{.}267\backslash \backslash$

$3$ & $1\mathrm{.}023$ & $0$ & $2\mathrm{.}575\backslash \backslash$

$4$ & $0\mathrm{.}729$ & $0$ & $2\mathrm{.}282\backslash \backslash$

$5$ & $0\mathrm{.}577$ & $0$ & $2\mathrm{.}115\backslash \backslash$

$6$ & $0\mathrm{.}483$ & $0$ & $2\mathrm{.}004\backslash \backslash$

$7$ & $0\mathrm{.}419$ & $0\mathrm{.}076$ & $1\mathrm{.}924\backslash \backslash$

$8$ & $0\mathrm{.}373$ & $0\mathrm{.}136$ & $1\mathrm{.}864\backslash \backslash$

$9$ & $0\mathrm{.}337$ & $0\mathrm{.}184$ & $1\mathrm{.}816\backslash \backslash$

$10$ & $0\mathrm{.}308$ & $0\mathrm{.}223$ & $1\mathrm{.}777\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

s$.$ Data Table

ounce

desi

roces

$\backslash$begin$\{$tabular$\}\{|$ccccc$|\}$

$\backslash$hline $\backslash$multicolumn$\{5\}\{$c$\}\{$ Question Viewer $\}\backslash \backslash$

$\backslash$cline $\{3-5\}$ & $\backslash$multicolumn$\{3\}\{$c$|\}\{$ Bottle $\}$ & $\backslash \backslash$

$\backslash$hline Sample & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )\backslash \backslash$

$\backslash$hline $1$ & $11\mathrm{.}94$ & $11\mathrm{.}95$ & $11\mathrm{.}93$ & $12\mathrm{.}12\backslash \backslash$

$2$ & $11\mathrm{.}93$ & $12\mathrm{.}10$ & $11\mathrm{.}93$ & $12\mathrm{.}08\backslash \backslash$

$3$ & $12\mathrm{.}10$ & $12\mathrm{.}12$ & $11\mathrm{.}98$ & $11\mathrm{.}98\backslash \backslash$

$4$ & $11\mathrm{.}88$ & $11\mathrm{.}93$ & $11\mathrm{.}94$ & $12\mathrm{.}07\backslash \backslash$

$5$ & $12\mathrm{.}01$ & $11\mathrm{.}86$ & $12\mathrm{.}01$ & $12\mathrm{.}07\backslash \backslash$

$6$ & $12\mathrm{.}10$ & $11\mathrm{.}98$ & $11\mathrm{.}91$ & $12\mathrm{.}07\backslash \backslash$

$7$ & $11\mathrm{.}90$ & $12\mathrm{.}12$ & $11\mathrm{.}86$ & $11\mathrm{.}94\backslash \backslash$

$8$ & $11\mathrm{.}92$ & $12\mathrm{.}05$ & $12\mathrm{.}07$ & $11\mathrm{.}88\backslash \backslash$

$9$ & $11\mathrm{.}90$ & $12\mathrm{.}02$ & $12\mathrm{.}10$ & $11\mathrm{.}95\backslash \backslash$

$10$ & $11\mathrm{.}88$ & $12\mathrm{.}12$ & $11\mathrm{.}94$ & $11\mathrm{.}98\backslash \backslash$

$11$ & $12\mathrm{.}13$ & $12\mathrm{.}08$ & $11\mathrm{.}88$ & $12\mathrm{.}11\backslash \backslash$

$12$ & $12\mathrm{.}08$ & $12\mathrm{.}08$ & $11\mathrm{.}98$ & $11\mathrm{.}87\backslash \backslash$

$13$ & $12\mathrm{.}01$ & $11\mathrm{.}95$ & $11\mathrm{.}86$ & $12\mathrm{.}09\backslash \backslash$

$14$ & $11\mathrm{.}99$ & $11\mathrm{.}97$ & $12\mathrm{.}10$ & $11\mathrm{.}90\backslash \backslash$

$15$ & $11\mathrm{.}88$ & $11\mathrm{.}94$ & $12\mathrm{.}08$ & $12\mathrm{.}02\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ The production manager at Sunny Soda, Inc., is interested in tracking the quality of the company's $12-$ounce bottle filling line. The bottles must be filled within the tolerances set ff $...\text{'}...$ cause the dietary information on the label shows $12$ ounces as the serving size. The design standard for the product calls for a fill level of $\backslash (12\backslash$pm $0\mathrm{.}10\backslash )$ ounces. $\backslash (\backslash$mathrm$\{$T$\}\_\{\backslash$text $\{\}\}\backslash )...$anaye cunected the accompanying sample data $($in fluid ounces per bottle$)$ on the production process.Click the icon to view the sample data.

Click the icon to view the table of factors for calculating three$-$sigma limits for the $\backslash (\backslash$overline$\{\backslash$mathrm$\{$x$\}\}\backslash )-$chart and R$-$chart.

Design an $\backslash ($ R $\backslash )-$ and an $\backslash (\backslash$bar$\{$x$\}\backslash )-$chart for this process.

The $\backslash ($ U C L$\_\{$R$\}\backslash )$ equals ounces and the $\backslash ($ L C L$\_\{$R$\}\backslash )$ equals ounces. $($Enter your responses rounded to three decimal places.$)$