$2.$ Consider the following processes:

$($i$)5-$sigma quality with $1\mathrm{.}5-$sigma off$-$centering.

$($ii$)3\mathrm{.}5-$sigma quality with $1\mathrm{.}0-$sigma off$-$centering.

a$)$ Draw the process distribution curves separately for the two processes. Clearly show the target value, process mean, USL and LSL with corresponding formulas $($you should include a screenshot$).$

b$)$ Compute defective rate and number of defective parts per million parts produced $($DPM or DPMO$)$ for each process. Which process has a better DPM$?$ Note: Show all your work, no credit will be given for answers only.