IS N = 30 BIG ENOUGH?

IS N = 30 BIG ENOUGH? A while back there was a discussion on the rule of thumb that a sample of size n=30 is sufficient in practice for assuming normality of the sample mean. Does anyone know the source of this "rule of thumb"? I recently responded to a High School student"s question on the same subject. Here is what I wrote: Bill Willis asks: The text book we are using says use the z- distribution when ever the sample size exceeds 30 and the distribution is normal. Let sample s approximate population sigma. How come the t- table in the AP booklet has degrees of freedom entries way past 30 ??? What am I missing??