Thinking about it more, it may be some problem with English rather than statistics....

again, the book says

"Regardless of the shape of the population, if a sufficiently large sample of size n is taken from the population, then the sample is approximately normally distributed....

If the book is correct (it seems wrong to me) then how do deal with sample being the ENTIRE population? Suppose our population is adults in the USA, and the variable is annual income. As the sample size approaches the population size, the distribution of the sample approaches the distribution of the population, which is highly skewed. If we have the whole population in the sample, then the distributions must be identical.

But what the CLM really says is that if we take REPEATED samples from the population then the distribution of the mean of the samples approaches normal as the number of samples approaches infinity

right?

Peter