An automatic filling machine is used to fill $1-$liter bottles of cola. The machine$$s output is approximately normal with a mean of $0\mathrm{.}99$ liter and a standard deviation of $0\mathrm{.}04$ liter. Output is monitored using means of samples of $26$ 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. $($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?

multiple choice $1$

Yes

No

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 $1\mathrm{.}004?$

multiple choice $2$

Yes

No