$8.($Process Capability when $\backslash$sigma is known$)$ A process that produces computer chips has a mean of $0\mathrm{.}04$ defective chip and a standard deviation of $0\mathrm{.}003$ chip. The allowable variation is from $0\mathrm{.}03$ to $0\mathrm{.}05$ defective. $($a$)$ Compute the capability index for the process. $($b$)$ Is the process capable? $9.($Process Capability when $\backslash$sigma is unknown$)$ In problem $8,$ suppose standard deviation is not known and we are provided with the following range data of the same process: $($a$)$ Compute the capability index for the process. $($b$)$ Is the process capable?