Suppose that a researcher is interested in estimating the mean systolic blood pressure, u, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate u. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 3 mm Hg of u?

Carry the intermediate computations to at least three decimal places. Write the answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).