Autopitch devices are made for both$$ major$-$ and$$ minor$-$league teams to help them improve their batting averages. When set at the standard$$ position, Autopitch can throw hardballs toward a batter at an average speed of $70$ mph$.$ To monitor these devices and to maintain the highest$$ 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$).$

Part $3$

LCL Subscript x overbarequals

$$

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

Part $4$

$$b$)$ Using this$$ information, construct control limits for the $$R$-$chart.

UCL Subscript Upper Requals

$$

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

Part $5$

LCL Subscript Upper Requals

$$

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