The median is greater than the mean, revealing left skewness attributable to the values 14.5 and 25.6. The first machine, although it produced one outlier, has far less variability, even though the critical dimension produced by each machine had nearly identical medians. Consider 3 overlapping circles for each part. U is an integer between 0 and 6 inclusive. Z is an integer between 0 and 2 inclusive.
Hypergeometric calculations are tedious.
Use the negative binomial distribution. The graph is a parabola, inverted. Use the approximation method on page 168. First obtain alpha and beta. Spreadsheet showing details to download here .