Elected officials in a small Florida town are preparing the annual budget for their community. Specifically, they would like to estimate how much their constituents living in this town are typically paying each year in real estate taxes. Given that there are over 3000 homeowners in this small community, officials have decided to sample a representative subset of taxpayers and thoroughly study their tax payments. The latest frame of homeowners is given in P8_36.XLS. 

a. What sample size would be required for elected officials to be approximately 95% sure that their estimate of the average annual real estate tax payment made by homeowners in their community is within $100 of the true mean? Assume that their best estimate of the population standard deviation o is $535. 

b. Choose a simple random sample of the size found in part a. 

c. Compute the observed sampling error based on the sample you have drawn from the population given in P8_36.XLS. How does the actual sampling error compare to the maximum probable absolute error established in part a? Explain.