Because the beadboard is stable and predictable, and follows a normal distribution, we can use the empirical rule to predict roughly how the beads will fall.
First of all, we need to gather data from a few subgroups in order to be able to estimate the process standard deviation (sigma). We set the board to use subgroups of size 5, and collected the following values:
| x1 | x2 | x3 | x4 | x5 | Mean | Range | |
|---|---|---|---|---|---|---|---|
| Group 1 | 13 | 15 | 16 | 14 | 17 | ||
| Group 2 | 15 | 15 | 14 | 15 | 15 | ||
| Group 3 | 16 | 16 | 15 | 17 | 14 | ||
| Group 4 | 13 | 16 | 16 | 17 | 16 | ||
| Group 5 | 17 | 13 | 16 | 16 | 16 |