Additional Algo $9-3$ Variance Reduction Targets

A drilling process has an upper specification of $1\mathrm{.}964$ millimeters and a lower specification of $1\mathrm{.}777$ millimeters. A sample of parts had a mean of $1\mathrm{.}87$ millimeters with a standard deviation of $0\mathrm{.}026$ millimeters.

What standard deviation will be needed to achieve a process capability index of $2\mathrm{.}0?$

Note: Round your answer to $5$ decimal places.

Standard deviation