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.