Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of

the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions $($in$.)$ from the last six samples are

Bottle

Click the icon to view the table of factors for calculating three$-$sigma limits for the $\stackrel{}{x}-$chart and $R-$chart.

Assume that only these six samples are sufficient, and use the data to determine control limits for an $R-$ and an $\stackrel{}{x}-$chart.

Compute the range $R$ and the sample mean $\stackrel{}{x}$ for each sample. $($Enter your responses rounded to three decimal places.$)$

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Factors for calculating three$-$sigma limits for the $\stackrel{}{x}-$chart and R$-$chart