$12)$ Using historic data from a process, with samples of size n$=4($from a time when the process was

considered to be in control$),$ a range chart was developed with LCL $=0$ and UCL $=2\mathrm{.}50.$ Similarly, an X$-$

bar chart was developed with an LCL of $15\mathrm{.}0$ and a UCL of $24\mathrm{.}0.$ Five $(5)$ new samples of size n$=4$ were then taken from the process. The means and ranges of the five samples are given in the table below. Is the process in control or not?

a$)$

b$)$

Both the process range and the process mean are in control.

Both the process range and the process mean are out of control.

c$)$

d$)$

The process mean is in control, but the process range is out of control.

We do not have enough information to determine if the process is in control or not.

Range of each sample

Mean of each sample

$1\mathrm{.}75$

$19\mathrm{.}5$

$2\mathrm{.}42$

$22\mathrm{.}3$

$2\mathrm{.}75$

$17\mathrm{.}4$

$2\mathrm{.}04$

$20\mathrm{.}1$

$2\mathrm{.}80$

$18\mathrm{.}9$