Given: A process has a mean of $75,$ and a standard deviation of $3.$ Spec limits are $70$ and $82.$

$1)$ What is the percent or proportion non$-$conforming?

$2)$ What is the sigma level?

$3)$ What is the DPMO?

Assume that the standard deviation was reduced to $1\mathrm{.}5$ via a DMAIIC Green Belt Project. If this was done at a cost of $$100,000,$ would it be worth it$,$ assuming a one year payback? Upload your work, and report the gross and net savings.