Question content area

Part $1$

Organic Grains LLC uses statistical process control to ensure that its$$ health$-$conscious, low$-$fat, multigrain sandwich loaves have the proper weight.

Based on a previously stable and$$ in$-$control process, the control limits of the x$-$ and$$ R$-$charts are:

UCLx $=6\mathrm{.}75,$ LCLx $=6\mathrm{.}45$;

UCLR $=1\mathrm{.}068,$ LCLR $=0.$

Over the past few$$ days, they have taken five random samples of four loaves each and have found the$$ following:

$$

Net Weight

Sample

Loaf$$ # $1$

Loaf$$ # $2$

Loaf$$ # $3$

Loaf$$ # $4$

$1$

$7\mathrm{.}4$

$7\mathrm{.}3$

$7\mathrm{.}2$

$7\mathrm{.}3$

$2$

$6\mathrm{.}6$

$6\mathrm{.}7$

$6\mathrm{.}6$

$6\mathrm{.}3$

$3$

$6\mathrm{.}1$

$6\mathrm{.}4$

$6\mathrm{.}1$

$6\mathrm{.}2$

$4$

$6\mathrm{.}5$

$6\mathrm{.}4$

$6\mathrm{.}6$

$6\mathrm{.}6$

$5$

$6\mathrm{.}2$

$6\mathrm{.}2$

$6\mathrm{.}1$

$6\mathrm{.}0$

Part $2$

Based on the x$-$chart, is one or more samples beyond the control$$ limits$?$

Yes

$.$

Part $3$

Based on the$$ R$-$chart, is one or more samples beyond the control$$ limits$?$

$$

No

Yes

$.$