One way to check the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known demographic facts about the population. About 12 percent of American adults are black. The number X of blacks in a random sample of 1500 adults should therefore vary with the B(1500, 0.12) distribution.
(a) What are the mean and standard deviation of X?
mean:180
standard deviation:12.58571
(b) Use the normal approximation to find the probability that the sample will contain 170 or fewer blacks. Be sure to check that you can safely use the approximation.