Chapter $10$: An automatic filling machine is used to fill $1-$liter bottles of cola. The machine$$s output is approximately normal with a mean of $1\mathrm{.}00$ liter and a standard deviation of $0\mathrm{.}03$ liter. Output is monitored using means of samples of $27$ 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.

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?