A normal probability curve shows the theoretical shape of a normally distributed histogram.  The shape of the normal probability curve is based on two parameters:  mean (average) and standard deviation (sigma).  The equation behind the normal probability curve itself is fairly complex, but defect-rate predictions are made easily by using normal probability tables (commonly known as z-tables).  The example below shows a a normal probability curve, fit to a histogram using MINTAB® software.

In the DMAIC world, normal distributions are used for making predictions and conducting certain hypothesis tests.  The 3.4 DPM rate associated with Six Sigma processes is based on the normal distribution curve.