Refer to the Control Chart Factor in your lecture notes for this problem.

A quality inspector took the following samples of the length of time$($in seconds$)$ for glue to dry. Please round your calculations to three decimal places.

Sample

Obs. $1$

Obs. $2$

Obs. $3$

Obs. $4$

Obs. $5$

$1$

$125$

$126$

$122$

$132$

$114$

$2$

$130$

$100$

$140$

$121$

$125$

$3$

$110$

$155$

$129$

$118$

$142$

$$

$$

$$a$)$ What is the value of x double overbar$?$

x double overbarequals

$$

$125\mathrm{.}933$ seconds $($round your response to three decimal$$ places$).$

$$b$)$ What is the value of Upper R overbar$?$

Upper R overbarequals

$$

$34\mathrm{.}333$ seconds $($round your response to three decimal$$ places$).$

$$c$)$ What are the UCL Subscript x overbar and LCL Subscript x overbar$?$

Upper Control Limit $($UCL Subscript x overbar$)=$

select: $145\mathrm{.}744$

$145\mathrm{.}744$ seconds $($round your response to three decimal$$ places$).$

Lower Control Limit $($LCL Subscript x overbar$)=$

select: $106\mathrm{.}123$

$106\mathrm{.}123$ seconds $($round your response to three decimal$$ places$).$

$$d$)$ What are the UCL Subscript Upper R and LCL Subscript Upper R$?$

Upper Control Limit $($UCL Subscript Upper R$)=$

select: $72\mathrm{.}615$

$72\mathrm{.}615$ seconds $($round your response to three decimal$$ places$).$

Lower Control Limit $($LCL Subscript Upper R$)=$

select: $0\mathrm{.}000$

$0\mathrm{.}000$ seconds $($round your response to three