[ska]

    You are saying: take enough of them and it is normal.

This doesn't completely undermine your point, but that isn't what they are saying, I think. I read it as saying by CLT that the estimates of the mean of those distributions is normal and centered on [the mean you are actually interested in]. Tails are perhaps somewhat a red herring here, because you don't really care about them unless you are specifically trying to evaluate worst-case-but-really-unlikely.

[mikekchar]

Yes, that is correct. It's been a very long time since I studied statistics, so I'm not sure if the variance of a mean has the same confidence interval as the mean. I suspect not. So you would indeed need to have a very large number of samples to get good error bars. It's a good point which I hadn't really considered. However it will never really get that far anyway because hopefully you'll intervene before the long tail hits you.

I think those really long tails are more of a problem when you are working with "features" that are much longer. If you have 1 day stories and you've been working on the story for a whole week, you know you have a massive problem. It's time to back up and see if there is a way to break it up, or to do it differently.

If you have a feature that is a month, by the time you get to 5 months, you have so much capital invested in the original plan that it's very hard (politically) to say, "Nope... this isn't working out. Let's try something else". Of course, it is very hard to get your organisation to plan to a 1 day level of granularity.