Right, I meant to say _approximately_ Normal. If you're writing it down
mathematically then the sample mean is only Normal if the larger
population is also Normal. But in practice, nothing is ever exactly
Normal anyway, so in that sense it's just a matter of when have you have
enough to get a good approximation to a Normal (if you're talking about
practical purposes that is...if instead the purpose is to answer an exam
question as to _exactly_ what the distribution is, you'd have to be given
the distribution of the larger population to be able to answer correctly).
Just out of curiousity, I'd like to know what kind of population you could
have such that a sample mean with N = 200 wouldn't be approximately
Normally distributed. That would have to be a very, very strange
distribution indeed.
On Fri, 21 Sep 2001, Gus Gassmann wrote:
> Joe Galenko wrote:
>
> > The mean of a random sample of size 81 from a population of size 1 billion
> > is going to be Normally distributed regardless of the distribution of the
> > overall population (i.e., the 1 billion). Oftentimes the magic number of
> > 30 is used to say that the mean will have a Normal distribution, although
> > that is when we're drawing from an infinitely large population. But for
> > the purposes of determining the distribution of a mean, 1 billion is
> > effectively infinite. And so, 81 is plenty.
>
> There are other issues. First off, if the underlying population is not normal,
> the sample mean will not be normal. Period. However, if the sample size
> is large, the distribution of the sample mean becomes _approximately_
> normal as the sample size increases. The question is at what point the
> difference from a normal distribution becomes so small as to be negligible.
> If the distribution is "nice", samples of size 10 may have reasonably
> well-behaved sample means. On the other hand, if the population is
> sufficiently awful, 200 points may not be enough. It just depends.
>
> -------------------------------------------------------
>
> gus gassmann ([EMAIL PROTECTED])
>
> "When in doubt, travel."
>
>
> Remove NOSPAM in the reply-to address
>
>
>
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