Problem $1($this is problem #$3$ in the textbook$)$

The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box$-$filling line to be set so that the process average weight per packet is $45$ grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of $10$ packets and weighs each packet. When the process is in control, the range in the weight of each sample has averaged $6$ grams.

a$.$ Design an $R-$ and an $\stackrel{}{x}-$chart for this process.

b$.$ The results from the last five samples of $10$ packets are

$\backslash$table$[[$Sample$,\stackrel{}{x},R$