An automatic filling machine is used to fill $1-$liter bottles of cola. The machine's output is approximately normal with a mean of $0\mathrm{.}96$ liter

and a standard deviation of $0\mathrm{.}05$ 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.

Note: Do not round intermediate calculations. Round $z$ value to $2$ decimal places. Round your answers to $4$ decimal places.

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?

No

Yes

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 $1\mathrm{.}004?$

No

Yes

Please help with homework PART A$,$B$,$C $!!$ will upvote if it helps me$!!!$