Assuming a standard normal distribution , you can use probability distributions to make predictions for outcomes of business processes by:
calculating the area under the curve that does not meet the business limits - defining how far away from the limit the process is (Z value). With known X=0, sd=1, and a limit
calculating the probability of the process not achieving or achieving the desired limits (DPMO) With known mean, sd, and limit
with known Z value (item 1) can convert to DPMO
with known DPMO (item 2) can convert to Z-value
Using the information to establish the business case and support the charter of a DMAIC to ensure we exceed the business goals.