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 of48male 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=7.80ml/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? (Round your answers to two decimal places.)

lower limit=

upper limit=

margin of error=

(b)

Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.00for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters=