Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, µ. 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 10.4 minutes, what is the minimum sample size needed for the managers to be 90% confident that their estimate is within 2.2 minutes of u? 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.)

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