In the production of a specific component with a target dimension of $25\mathrm{.}0mm,$a manufacturing process has been monitored using $30$ sample measurements collected from the production line. The upper specification limit $($USL$)$ for the component is $25\mathrm{.}2mm,$ the lower specification limit $($LSL$)$ is $24\mathrm{.}8mm$ and the sample standard deviation is $0\mathrm{.}22.$ The data for the measurement is given in Table $1.$

Table $1$: Measurement Data

$\backslash$table$[[$Measurement Data$/$ Data Pengukuxan$],[25\mathrm{.}2,24\mathrm{.}8,25\mathrm{.}1,25\mathrm{.}0,25\mathrm{.}3],[24\mathrm{.}9,25\mathrm{.}2,25\mathrm{.}1,24\mathrm{.}8,25\mathrm{.}0],[25\mathrm{.}2,25\mathrm{.}3,25\mathrm{.}0,25\mathrm{.}1,24\mathrm{.}9],[25\mathrm{.}2,24\mathrm{.}8,25\mathrm{.}0,25\mathrm{.}3,25\mathrm{.}1],[24\mathrm{.}9,25\mathrm{.}2,25\mathrm{.}0,25\mathrm{.}3,25\mathrm{.}1],[24\mathrm{.}9,25\mathrm{.}2,25\mathrm{.}0,25\mathrm{.}3,25\mathrm{.}1]]$

$($a$)$ Calculate the Sample Mean

$($b$)$ Calculate the Cp index

$($c$)$ Calculate the Cpk index

$($d$)$ Explain if the process meets specifications and identify areas for improvement.

$(4)$

$($ Total $/$ Jumlah: $20)$