Hello,
I have a question regarding the so-called normal approx. to the binomial
distribution. According to most textbooks I have looked at (these are
undergraduate stats books), there is some talk of how a binomial random
variable is approximately normal for large n, and may be approximated by the
normal distribution. My question is, are they saying that the sampling
distribution of a binomial rv is approximately normal for large n?
Typically, a binomial rv is not thought of as a statistic, at least in these
books, but this is the only way that the approximation makes sense to me.
Perhaps, the sampling distribution of a binomial rv may be normal, kind of
like the sampling distribution of x-bar may be normal? This way, one could
calculate a statistic from a sample, like the number of successes, and form
a confidence interval. Please tell me if this is way off, but when they say
that a binomial rv may be normal for large n, it seems like this would only
be true if they were talking about a sampling distribution where repeated
samples are selected and the number of successes calculated.
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