QUESTION $17$

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

$0\mathrm{.}93$ liters and a standard deviation of $0\mathrm{.}02$ liter. Output is monitored using means of samples of $29$ observations. Use z$-$tables to

answer the question.

$($a$)$ Determine the standard error of the mean.

$($round your answer to $5$ decimal places$)$

$s.e.=$

$($b$)$ 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 your answers to $4$ decimal places.$)$

Upper control limit $=$

Lower control limit $=$

$($c$)$ Given these sample means: $1\mathrm{.}005,1\mathrm{.}001,\mathrm{.}998,1\mathrm{.}002,\mathrm{.}995,$ and $\mathrm{.}999,$ is the process in control?

Write either "Yes" or $"$No$"$ in the response box below