Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, u. The managers plan to choose a random sample of completion times and estimate u via the sample. Assuming that the standard deviation of the population of completion times is 10.2 minutes, what is the minimum sample size needed for the managers to be 99% confident that their estimate is within 1.5 minutes of j? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) X