Conduct a study to determine how well the binomial distribution approximates the hypergeometric distribution. Consider a bag

Question:

Conduct a study to determine how well the binomial distribution approximates the hypergeometric distribution. Consider a bag with n balls, 25% of which are red. A sample of size (0.10)n is taken. Let X be the number of red balls in the sample. Find P(X ≤ (0.02)n) for increasing values of n when sampling is

(i) With replacement and

(ii) Without replacement. Use R.

Distribution
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