Apparently you have never popped popcorn, because a Poisson process it is not. The events are not randomly distributed in time according to some fixed rate - you put the kernels in the oil, wait a while, then all the kernels pop at once in a narrow time interval. The time to pop is a function of variability in the kernels and heating, not pure stochasticity. This should be modeled by a normal distribution, not a Poisson.
