Problem $2$

Suppose that your business is operating at the Three Sigma quality level. If projects have an average improvement rate of $75\%$ annually, how many years will it take to achieve Six Sigma quality?

Note: A Six Sigma quality level produces no more than $3\mathrm{.}4ppm($defect parts or defects per million opportunities to make a defect$).$ A Three Sigma quality level produces no more than $66,810ppm($defect parts or defects per million opportunities to make a defect$).$