The time needed for performing a machining operation is to be investigated. Historically, the process has had a standard deviation equal to $0\mathrm{.}165$ minutes. The means $($in minutes$)$ of $39$ samples of n $=6$ are:

Sample Mean Sample Mean Sample Mean

$13\mathrm{.}89143\mathrm{.}72273\mathrm{.}88$

$23\mathrm{.}89153\mathrm{.}95283\mathrm{.}82$

$33\mathrm{.}74163\mathrm{.}78293\mathrm{.}55$

$43\mathrm{.}91173\mathrm{.}80303\mathrm{.}75$

$53\mathrm{.}88183\mathrm{.}91313\mathrm{.}87$

$63\mathrm{.}79193\mathrm{.}98323\mathrm{.}73$

$73\mathrm{.}72203\mathrm{.}72333\mathrm{.}97$

$83\mathrm{.}73213\mathrm{.}88343\mathrm{.}57$

$93\mathrm{.}94223\mathrm{.}79353\mathrm{.}85$

$103\mathrm{.}92233\mathrm{.}72363\mathrm{.}72$

$113\mathrm{.}72243\mathrm{.}91373\mathrm{.}68$

$123\mathrm{.}98253\mathrm{.}81383\mathrm{.}79$

$133\mathrm{.}92263\mathrm{.}91393\mathrm{.}95$

The average of the $39$ sample means is equal to $3\mathrm{.}82.$

a$.$ Construct an x$$

$-$chart for this process with two$-$sigma limits$.($Round the final answers to $2$ decimal places.$)$

UCL LCL

Mean Control Limits

b$.$ Is the process in control?

multiple choice

Yes

No