Q$6.$ A manufacturing company produces part A where its thickness is critical size as the part will be assembled with another part B$.$ The manufacturing process produces part A with a mean thickness of $7\mathrm{.}5cm$ and standard deviation of $0\mathrm{.}05cm.$ In order to achieve a perfect fit between the two parts, the thickness specification for Part $A$ is set to $7\mathrm{.}5+-0\mathrm{.}15.$ Anything outside the specification limits will create a misfit and part $A$ is sent back for a rework. $($Assume the thickness is normally distributed$)$

At what sigma level the process is currently performing

What is the percentage in ppm of part A that needs rework. $($use centered at target normal distribution$)$

What would be the standard deviation if the company would like to achieve six sigma level performance?