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 population standard deviation is $2\mathrm{.}15.$ The data from that activity appear below.

Weight

Day

Package $1$

Package $2$

Package $3$

Package $4$

Monday

$32$

$26$

$24$

$34$

Tuesday

$18$

$28$

$27$

$22$

Wednesday

$33$

$17$

$25$

$30$

Thursday

$18$

$22$

$26$

$17$

Friday

$28$

$20$

$24$

$19$

a$.$ What is the mean of all the sample means?

$24\mathrm{.}50$

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

$21\mathrm{.}45,18\mathrm{.}65$

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

no

d$.$ Calculate upper and lower limits for R$-$chart.

$24\mathrm{.}65,0$

e$.$ Is the range chart in control?

yesbar chart, is this process in control?

$[$ Select $]$

d$.$ Calculate upper and lower limits for R$-$chart.

$[$ Select $]$

e$.$ Is the range chart in control?

$[$ Select $]$