CHALLENGE How large a sample is needed? The changing probabilities you found in Exercises 5.22 and 5.24 are due to the fact that the standard deviation of the sample proportion

ˆp gets smaller as the sample size n increases. If the population proportion is p = 0.49, how large a sample is needed to reduce the standard deviation of ˆp to σˆp = 0.004? (The 68–95–99.7 rule then says that about 95% of all samples will have ˆp within 0.01 of the true p.)