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 of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.80 ml/kg for 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 27.32 X upper limit 33.68 X margin of error 3.18 (b) What conditions are necessary for your calculations? (Select all that apply.) o is known the distribution of volumes is normal n is large the distribution of volumes is uniform O . is unknown X (c) Interpret your results in the context of this problem. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval. We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters