Sample

$$Size$,$ n

Mean$$ Factor,

A$2$

Upper$$ Range,

D$4$

Lower$$ Range,

D$3$

$2$

$1\mathrm{.}880$

$3\mathrm{.}268$

$0$

$3$

$1\mathrm{.}023$

$2\mathrm{.}574$

$0$

$4$

$0\mathrm{.}729$

$2\mathrm{.}282$

$0$

$5$

$0\mathrm{.}577$

$2\mathrm{.}115$

$0$

$6$

$0\mathrm{.}483$

$2\mathrm{.}004$

$0$

$7$

$0\mathrm{.}419$

$1\mathrm{.}924$

$0\mathrm{.}076$

$8$

$0\mathrm{.}373$

$1\mathrm{.}864$

$0\mathrm{.}136$

$9$

$0\mathrm{.}337$

$1\mathrm{.}816$

$0\mathrm{.}184$

$10$

$0\mathrm{.}308$

$1\mathrm{.}777$

$0\mathrm{.}223$

$12$

$0\mathrm{.}266$

$1\mathrm{.}716$

$0\mathrm{.}284$

Autopitch devices are made for both$$ major$-$ and$$ minor$-$league teams to help them improve their batting averages. When set at the standard$$ position, Autopitch can throw hardballs toward a batter at an average speed of $66$ mph$.$ To monitor these devices and to maintain the highest$$ quality, Autopitch executive Neil Geismar takes samples of $12$ devices at a time. The average range is $5$ mph$.$

Part $2$

$$a$)$ Using this$$ information, construct control limits for the x overbar$-$chart.

UCL Subscript x overbarequals

$$

enter your response here mph $($round your response to three decimal$$ places$).$