A large construction contractor is building 257 homes, which are in various stages of completion. For tax purposes, the contractor needs to estimate the total dollar value of its inventory due to construction in progress. The contractor randomly selects (without replacement) a sample of 40 of the 257 houses and determines the accumulated costs (the amount of money tied up in inventory) for each sampled house. The contractor finds that the sample mean accumulated cost is  = $75,162.70 and that the sample standard deviation is s = $28,865.04.
a. Find a point estimate of and a 99 percent confidence interval for the total accumulated costs (total amount of money tied up in inventory) for all 257 homes that are under construction.
b. Using the confidence interval as the basis for your answer, find a reasonable estimate of the largest possible total dollar value of the contractor's inventory due to construction in progress.