Very few things in the real world have continious variables, we count and measure things as integers (number failures, boxes leaving shipping, etc). However, if you look at the Poisson distsribution, which is for discrete variables (not continous), as the frequency per interval rises (lambda in the link), you see if you "connect" the dots, it very much approaches the Normal distribution. The math on the Normal distribution is much easier, as calculus can be used to find the area under the graph (cumulative probability). So in the Real world, even when we deal with real countable objects, we can use the Normal distribution even we do not have continous variables (if the incidence for each event is measured over a large number of events.
So much for philosophy: However, you can see from this arguement, the normal distribution can be used for number of boxes expected per hour, cars on a bridge per hour, and etc, even though these are not continous variables.
I would pick the following: Error rate on keyboard entries, or time to type 100 words by data transcribers, or just anything like that.