Using a simple model, I have produced an output distribution as
rv = scipy.stats.johnsonsu(1.874, 2.324, 52.633, 1.097)
If this is a manufacturing setting, and my lower spec limit is 45 and upper spec limit is 55, I want to know the expected failure rates (x < 45 or x > 55). I can check the cumulative density function and the survival function, respectively, to perform each of the single tailed tests:
>>> rv.cdf(45) 1.035e-05 >>> rv.sf(55) 3.564e-08
Since this random variable represents an independent draw during manufacturing, if I assemble 1e6 units, should I expect none of them will be larger than 55 but 10 will be less than 45?