please show how they got the answer If the Cp value is greater than $1,$ it indicates that the process is capable of meeting the specifications. If it's less than $1,$ it suggests that the process might not consistently meet the specifications. Let's calculate: Cp$=(363350)/(6\backslash$times $2)$ Cp$1\mathrm{.}08$ The Cp value is greater than $1,$ which indicates that the process is capable of meeting the specifications.

However, to further assess the capability of the process, we can also calculate the process performance index

$($Cpk$),$ which considers both the centering of the process mean and the spread of the process.

Cpk$=$min$(($Upper specification limit$$Average$)/(3\backslash$times Standard deviation$),($Average$$Lower specification limit$)/(3\backslash$times Standard deviation$))$

Let's calculate: Cpk$=$min$((363355)/(3\backslash$times $2),(355350)/(3\backslash$times $2)$ Cpk$=$min$(1\mathrm{.}33,0\mathrm{.}83)$ Cpk$=$min$(1\mathrm{.}33,0\mathrm{.}83)$ Cpk$=0\mathrm{.}83$ Since the Cpk value is less than $1,$ it suggests that the process mean is not perfectly centered within the specification limits$.$ However, since the Cp value is greater than $1,$ it indicates that the process is capable of producing within the specified range, though it may not consistently do so with the mean perfectly centered. In conclusion, while the automated machine filling operation can meet the design specifications, there may be some variability in the volume of the bottles, with the mean slightly off$-$center. Further adjustments or monitoring may be needed to ensure consistent compliance with the specifications.

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