A quality analyst wants to construct a control chart for controlling a packaging process. Each day last week, he randomly selected four packages and weighed each. The data from that activity appear below.

$($a$)$ Which chart$($s$)$ would be appropriate to use for this process? Why?

$($b$)$ Calculate all sample means, sample ranges, the mean of all sample means, and the average range.

$($c$)$ Calculate upper and lower $3-$sigma x$-$bar chart control limits that allow for natural variations.

$($d$)$ Based on the x$-$bar chart, is this process in control?

$($e$)$ Calculate upper and lower $3-$sigma R chart control limits that allow for natural variations.

$($f$)$ Based on the R chart, is this process in control?