Quality Control (SPC) for a lottery-odds check

Statistical process control watches a process over time against control limits set at three standard deviations from the target. Points inside are normal random variation — leave them alone. A point beyond the limits, or a run trending one way, signals a real change worth investigating. Nudge the process shift and watch points breach the limits.

Cp compares the spec width to the process spread — can the process fit inside the tolerances at all? Cpk also accounts for how well-centered it is. A Cpk of 1.33 is the usual bar for capable; 2.0 is Six Sigma quality with just 3.4 defects per million. Widen the spread or push the mean off-center and defects climb fast.

A hypothesis test asks whether a sample mean is far enough from the null value to be surprising by chance alone. The test statistic z measures that distance in standard errors; if it falls in the red rejection region (p below 0.05) we reject the null. Larger samples shrink the standard error and sharpen the test.