7.35 Tax Savings An important expectation of a federal income tax reduction is that consumers will reap a substantial portion of the tax savings. Suppose estimates of the portion of total tax saved, based on a random sampling of 35 economists, have a mean of 26% and a standard deviation of 12%.

a. What is the approximate probability that a sample mean, based on a random sample of n = 35 economists, will lie within 1% of the mean of the population of the estimates of all economists?

b. Is it necessarily true that the mean of the popula- tion of estimates of all economists is equal to the percentage of tax savings that will actually be achieved? Why?