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Sampling without Replacement:
- Suppose a population contains a proportion p of successes. If the population is much larger than the sample size n, then given X = the number of successes observed in the sample
X will have an approximate binomial distribution.
i.e. X ~ approx. B(n,p).
- The accuracy of the approximation improves as the size of the population increases relative to the size of the sample.
Rule of Thumb: X ~ B(n, p) will be a very good approximation when the population is at least 20 times larger than the sample size.