please solve showing exact steps include all numbers and step by step to how you sovled in section Given Data:

Average volume: $355$ milliliters

Standard deviation: $2$ milliliters

Target volume range: $350-363$ milliliters

Process Capability Indices:

The process capability indices are calculated using the following formulas:

Lower process capability index $($Cpl$)$:Cpl$=3\backslash$times Standard$$deviationAverage$$volume$$Target$$min$$

Upper process capability index $($Cpu$)$:Cpu$=3\backslash$times Standard$$deviationTarget$$max$$Average$$volume$$

Calculations:

Lower process capability index:Cpl$=3\backslash$times $2355350=0\mathrm{.}8333$

Upper process capability index:Cpu$=3\backslash$times $2363355=1\mathrm{.}3333$

Conclusion:

The absolute values of both process capability indices are greater than or equal to $1.$

Therefore, the automated machine filling operation is not capable of meeting the design specifications.

In summary, the machine$$s variability exceeds the acceptable range specified by the design, indicating that adjustments or improvements are needed to ensure consistent filling within the desired volume limits$.$