Additional Algo $9-3$ Variance Reduction Targets

A milling process has an upper specification of $1\mathrm{.}525$ centimeters and a lower specification of $1\mathrm{.}48$ centimeters. A sample of parts had a mean of $1\mathrm{.}51$ centimeters with a standard deviation of $0\mathrm{.}02$ centimeters.

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

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

Answer is complete but not entirely correct.

$0\mathrm{.}37500$