For work I need to estimate how a group of 160 people would be divided among 5 sub-groups. Let's assume that the group conforms to a normal distribution.
I need to split the group by expected output (productivity) in 5 subgroups according to their output. I.o.w. if productivity is rated 1 to 5, one would expect a big group in the middle with a score of 3, and less peple with 2, 4 or some extremes with 1 or 5. Then I need to match this projection against the reality.
The 1,2,3 sigma rule doesn't help in this case because the mapping doesn't match.
There are tons of articles on Internet on how to calculate sigma based on data, but not on estimating population groups. University is a long time away, and I don't feel like digesting all the stuff again for only one estimation. I vaguely remember something about a z table. Would someone know how I can estimate how many people would fall in each of the 5 groups? Thanks!
Found a handy calculator here: http://davidmlane.com/hyperstat/z_table.html
I entered the mean of 2.5, an s of 1 and then the groups one by one. Distribution per group: 1: 6%, 2:24%,3:38%, 4:24%, 5:6%