A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:

Machine Measurements

#$117151517$

#$216251825$

#$323242322$

What are the x$-$bar chart three$-$sigma upper and lower control limits$?$

$23\mathrm{.}5$ and $16\mathrm{.}5$

$24$ and $16$

$23\mathrm{.}16$ and $16\mathrm{.}84$

$22$ and $18$

$23\mathrm{.}29$ and $16\mathrm{.}71$