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 of46male 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=7.20ml/kgfor the distribution of blood plasma.

Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.80for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)