dimensions $($in$.)$ from the last six samples are

$\backslash$table$[[$Bottle$],[$Sample$,1,2,3,4],[1,0\mathrm{.}574,0\mathrm{.}574,0\mathrm{.}610,0\mathrm{.}609],[2,0\mathrm{.}625,0\mathrm{.}582,0\mathrm{.}609,0\mathrm{.}609],[3,0\mathrm{.}599,0\mathrm{.}594,0\mathrm{.}622,0\mathrm{.}620],[4,0\mathrm{.}592,0\mathrm{.}577,0\mathrm{.}619,0\mathrm{.}584],[5,0\mathrm{.}599,0\mathrm{.}572,0\mathrm{.}610,0\mathrm{.}592],[6,0\mathrm{.}613,0\mathrm{.}578,0\mathrm{.}573,0\mathrm{.}625]]$

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Suppose that the specification for the bottle neck diameter is $0\mathrm{.}600+-0\mathrm{.}050in.$ and the population standard deviation is $0\mathrm{.}015$ in$.$

a$.$ What is the process capability index?

The $C_{pk}$ is $.($Enter your response rounded to two decimal places.$)$