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Answer:
Step-by-step explanation:
If repeated sample sizes of large sizes are taken at random, and proportion P is calculated for samples the sample mean will have a normal distribution irrespective of the original distribution.
In other words, the sample proportion will follow a normal distribution with mean = p-hat and std deviation =
This is a direct corrollary of central limit theorem for sample means.
Hence we have irrespective of sample size, sample proportion will have expected value same as p-hat.
So whether sample size is 500 or 100 the p hat will have the same distribution.