Question: Suppose that a simple random sample of size n is taken from a finite population in which the proportion of members having a specified attribute

Suppose that a simple random sample of size n is taken from a finite population in which the proportion of members having a specified attribute is p. Let X be the number of members sampled that have the specified attribute.

a. If the sampling is done with replacement, identify the probability distribution of X.

b. If the sampling is done without replacement, identify the probability distribution of X.

c. Under what conditions is it acceptable to approximate the probability distribution in part (b) by the probability distribution in part (a)? Why is it acceptable?

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