Problem $10-2($Algo$)$

An automatic filling machine is used to fill $1-$liter bottles of cola. The machine's output is approximately normal with a

mean of $1\mathrm{.}00$ liter and a standard deviation of $0\mathrm{.}05$ liter. Output is monitored using means of samples of $25$ 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?

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 $1\mathrm{.}004?$

Yes

No