I hold that the Poisson distribution is not justified for a number of factors, including variation in hash rate, geographics and clustering (nonuniformity) of block finds.
I am spending so much time on this because I am generally interested from the standpoint of altcoin development. Thus modeling the block chain is an interesting topic.
Variation of hash rate indeed would violate the Poisson assumption of "the average frequency of occurrence for the time period in question is known". I don't understand how you think geographics affects the model? Isn't clustering modeled by Poisson?
I also hold that you can choose any consecutive 12 gaps and you will get a probability within a factor of 5 from your example's with confidence over 90%.
90% of the time? Really? That is profound. Then we should be able to look at any 120 minutes and find 9 occurrences most of the time.
Wait I will find a block chain explorer and verify your claim anecdotally. BRB...