An educator is interested in the mean IQ in a given population (say, the freshman class at a certain university). He cannot afford to test the entire population, but he is willing to assume that IQ is normally distributed with variance 121 in the population of interest. He wants to take a random sample of members of the population in order to determine a 90 percent confidence interval for mean IQ. How large a sample will he need if he wants the length of the confidence interval to be no greater than 5? If he wants the length to be no greater than 1 ?