According to DoSomething.org and Facts.randomhistory.com approximately 46% of all the lakes in America are too polluted for fishing, aquatic life, or swimming. You are not sure that this percentage is accurate. You decide to gather some sample data to get your own estimate for the proportion of lakes in American that are too polluted for fishing, aquatic life, or swimming.

a) What sample size would be needed for the estimate to be within 3 percentage points with 95% confidence if you don't use the percentage from DoSomething.org?

b) You decide to take a random sample of 1022 lakes and you discover that 513 of them are too polluted for fishing, aquatic life, or swimming. Construct a 95% confidence interval for the proportion of lakes that are too polluted for fishing, aquatic life, or swimming. Round 3 decimals.

c) Interpret the interval.

d) Based on your confidence interval is it possible that proportion of lakes that are too polluted for fishing, aquatic life, or swimming is 0.46 or less? Do you think this is likely? Explain using a complete sentence.