Question $1(2$ points$)$

An automatic filling machine is used to fill $2-$litres bottles of cola. The machine's output is known to be approximately Normal with a mean of $1\mathrm{.}0$ liter and a standard deviation of $0\mathrm{.}007$ liters. Output is monitored using means of samples of ten observations.

a$.$ Determine the upper and lower control limits that will include roughly $95\mathrm{.}44$ percent of the sample means $($Consider $z=2$ for $95\mathrm{.}44$ percent of the sample means and round the final answers to $3$ decimal places$).$

b$.$ If the means for $6$ samples are $\mathrm{.}996,\mathrm{.}992,1\mathrm{.}002,\mathrm{.}994,1\mathrm{.}004,$ and $\mathrm{.}992,$ is the process in control?