Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of47male firefighters are tested and that they have a plasma volume sample mean ofx= 37.5 ml/kg(milliliters plasma per kilogram body weight). Assume that=8.00ml/kgfor the distribution of blood plasma.

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Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.80for the mean plasma volume in male firefighters.