$(5$ points$)$ A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of $22\mathrm{.}9mm$ and an upper specification limit of $23\mathrm{.}5mm.$ The standard deviation is $0\mathrm{.}11mm$ and the mean is $23\mathrm{.}2mm.$

What is the process capability index for the process? $($Round your answer to $4$ decimal places.$)$ You must show final answer only.