Elected officials in a California city are preparing the annual budget for their community. They would like to estimate how much their constituents living in this city are typically paying each year in real estate taxes. Given that there are over 100,000 homeowners in this city, the officials have decided to sample a representative subset of taxpayers and study their tax payments. a. What sample size is required to generate a 95% confidence interval for the mean annual real estate tax payment with a half-length (margin of error) of $100? Assume that the best estimate of the population standard deviation is $535. b. lf a random sample of the size from part a is selected and a 95% confidence interval for the mean is calculated, will the margin of error be equal to $100? Why or why not? c. Now, suppose that the officials want to construct a 95% confidence interval with margin of error of $75. What sample size is required? Assume the same standard deviation as in parta. d. If the city officials want to determine the proportion of taxpayers that pay their taxes, how many residents will they need to survey if they want to margin of error to be 1%?