Capability for discrete data, not sure what distribution is called

I'm trying to do capability analysis on the count of items dispensed. The values are discrete since I cannot have 1.2 items dispensed. The trouble is that when I do a capability analysis the predicted performance is way worse than the observed. The spec is 12 +/- 2 items.

A couple of questions:

1. What is the name for this kind of distribution, where any integer is allowed but not the probability is not uniform?
2. If this is indeed not normal, do I do a transform? I used Minitab and I only discrete distribution option I see are binomial and poisson.