$[10$ points$]$ Suppose that a quality characteristic is normally distributed with

specifications at $150+-20.$ Natural tolerance limits for the process are $150+-18.$

$($a$)$ Calculate the process standard deviation.

$($b$)$ Calculate PCR and $PC{R}_k$ of the process. Calculate the percentage of the specification

width used by the process.solve

$($Solve problems either through hand calculations or R code. Hand calculations means any method

other than R coding. You can show work via excel, typing on word document etc. if you do not

use R code