5.76 How large a sample is needed? The changing probabilities you found in Exercise 5.74 are due to the fact that the standard deviation of the sample proportion p^ gets smaller as the sample size n increases. If the population proportion is p=0.41 , how large a sample is needed to reduce the standard deviation of p^ to

σp^=0.005

? (The 68–95–99.7 rule then says that about 95% of all samples will have p^ within 0.01 of the true p.)