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 of50male 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=7.10ml/kgfor the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Lower and upper limit, margin of error)

(c) Interpret your results in the context of this problem.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.10for the mean plasma volume in male firefighters.