From the lecture we learned that natural process variability is the variability that we expect to face in our normal production environment. This natural variability is defined as $+/-3\backslash$sigma from the mean, which is equivalent to $99\mathrm{.}73\%$ of the production $($property of a normally distributed variable$).$Comparing this natural process variability $($represented by $+/-3\backslash$sigma to the specification limits gives us a measure for our $$Process Capability.$$

$2$a$.$ A cable manufacturer produces micro USB cables.

The size of the connector is allowed to vary between $4\mathrm{.}998$ mm and $5\mathrm{.}002$ mm$.$

The process is currently centered between the specifications and is running with a standard deviation $(\backslash$sigma $)$ of $0\mathrm{.}001$ mm$.$

What is the CPK value of the connector size for this process?