A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is $2$ ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appear below.

Weight

Day Package $1$ Package $2$ Package $3$ Package $4$

Monday $23222320$

Tuesday $23211921$

Wednesday $20222021$

Thursday $18192017$

Friday $18202222$

$($a$)$ Calculate the mean of all sample means.

$($b$)$ Calculate upper and lower control limits that include $99\%$ of the sample means.

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

Group of answer choices

$22\mathrm{.}96$ and $17\mathrm{.}05$

$22\mathrm{.}62$ and $17\mathrm{.}37$

$21\mathrm{.}59$ and $17\mathrm{.}88$

$23\mathrm{.}13$ and $17\mathrm{.}97$

Flag question: Question $9$