An automatic filling machine is used to fill $1-$liter bottles of cola. The

machine's output is approximately normal with a mean of $0\mathrm{.}99$ liter and

a standard deviation of $0\mathrm{.}04$ liter. Output is monitored using means of

samples of $28$ observations. Use Table$-$A$.$

a$.$Determine upper and lower control limits that will include roughly $97$

percent of the sample means when the process is in control. $($Do not

round intermediate calculations. Round $z$ value to $2$ decimal places.

Round your answers to $4$ decimal places.$)$

Upper control limits:

liter

Lower control limits:

liter

b$.$Given these sample means: $1\mathrm{.}005,1\mathrm{.}001,\mathrm{.}998,1\mathrm{.}002,\mathrm{.}995,$ and $\mathrm{.}999,$

is the process in control?

Yes

No