$2.$ An automatic filling machine is used to fill $1$ litre bottles of cola. The machine$$s output is approx.

normal with mean of $1\mathrm{.}0$ lit and S$.$D$.$ of $0\mathrm{.}01$ lit. Output is monitored using means of samples of

$25$ observations.

$($i$)$ Determine UCL & LCL that will include roughly $97\%$ of the sample means when the process is

in control?

$($ii$)$ Given these sample means: $1\mathrm{.}005,1\mathrm{.}001,0\mathrm{.}998,1\mathrm{.}002,0\mathrm{.}995$ & $0\mathrm{.}999,$ is the process in

control?