[hessenwolf]

n greater than 30:

A quantity that follows normal distribution has two things to estimate, the variability of the quantity (standard deviation), and the mean. Both of these are estimated with uncertainty from a series of observations of the quantity (the data). The t-distribution allows us to make predictions, taking into account both sources of uncertainty for a normally distributed thing.

However, as the number of observations increases towards thirty, the estimate of the standard deviation gets really, really good, so you can happily ignore the uncertainty for that. Then you just need the normal distribution.

[grayclhn]

That is hugely misleading. It's only reasonable if the data are actually independent draws from a normal distribution. IRL, they're not.