Now that we know about the empirical distribution of block times, what would the confirmation times look like?
WARNING: This does not take into account the difficulty adjustments that arise when blocks are off the average block time. This means that in reality the standard deviation of multiple confirmations will not increase so much.
How about a Monte Carlo Simulation? The Result is: The distribution of confirmation times gains high variability when you wait for more. You are not only trading safety for speed, but also safety for certainty.
For a better assessment of the quantiles here a boxplot. Obviously, the distribution becomes more symmetrical the more time we wait.