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

Sample

$1$

$2$

$3$

$4$

$1$

$2$

$3$

$4$

$5$

$6$

LOADING... Click the icon to view the table of factors for calculating$$ three$-$sigma limits for the $-$chart and$$ R$-$chart.

Part $2$

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

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

Bottle

Sample

$1$

$2$

$3$

$4$

R

$1$

$2$

$3$

$4$

$5$

$$

enter your response here

$$

enter your response here

$6$

$$

enter your response here

$$

enter your response here