Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of tis moeny is put int a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 222.0. Summary statistics yield X-bar (aka the mean)= 180.975 and S = 143.042.a.) Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. b.) Calculate a 99% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.