You draw a random sample of n = 500 from a population with a standard deviation of 51.5. The sample mean is 212.

a) Calculate a confidence interval for the population mean at a 99% confidence level. Round your answer to 3 decimal places.

b) Interpret your confidence interval in context.

c) What is the margin of error for your confidence interval?

d) What two things could you do (or could you have done) to decrease the margin of error?

e) Why is it incorrect to say that "there is a 99% chance that the population parameter falls inside the confidence interval"? Explain.