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 mi/kg (milliliters plasma per kilogram body weight). Assume that @ = 7.40 mi/kg for the distribution of blood plasma. (a) Find the margin of error for a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Round your answer to two decimal places.) ml/kg Find a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.) ml/kg (b) What conditions are necessary for your calculations? (Select all that apply.) [ nis large [J the distribution of volumes is normal U the distribution of volumes is uniform [ o is unknown O o is known (c) Interpret your results in the context of this problem O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. D 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 0.99. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error = 2.60 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) : male firefighters