$2.$ An automatic filling machine is used to fill $1-$liter bottles of cola. The machine$$s output is approximately$$normal with a mean of $1\mathrm{.}0$ liter and a standard deviation of $\mathrm{.}01$ liter. Output is monitored$$using means of samples of $25$ observations.$$a$.$ Determine upper and lower control limits that will include roughly $97$ percent of the sample$$means when the process is in control.$$b$.$ Given the following sample means$1\mathrm{.}005,1\mathrm{.}001,\mathrm{.}998,1\mathrm{.}002,\mathrm{.}995,$ and $\mathrm{.}999$is the process in$$control$?$c$.$ Is the process in control given the following sample means$1\mathrm{.}003,\mathrm{.}999,\mathrm{.}997,1\mathrm{.}001,1\mathrm{.}002,\mathrm{.}998,$ and $1\mathrm{.}004?$