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RolfAndreassen comments on Punctuality - Arriving on Time and Math - Less Wrong Discussion
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The 102 version of this class would observe that the distribution is unlikely to be really Gaussian on the tails. There's presumably zero probability that you arrive for an important meeting three days late; conversely there's some nonzero probability that you don't show up at all because you were hit by a bus. But obviously the Gaussian is a fine approximation for most practical risk levels.
I'm not so sure it is a fine approximation, though of course it's better than nothing. There's most likely considerable skew to the right -- it's much easier for an unexpected event to delay you a lot than to speed you up a lot -- so the mode (which I think is nearer to what most people think of if they aren't explicitly considering the distribution) is substantially earlier than the mean or median. Empirically, IIRC there's good evidence that asking people to predict best-case completion times for projects gets more or less identical results to asking them to predict typical completion times.
I once showed up for a meeting a week early.