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 ov_erall health and physical activity of an individual. Suppose that a random sample of 48 male 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 0 = 7.00 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.) lowernmn E margin of error :] (b) What conditions are necessary for your calculations? (Select all that apply.) [1 n is large [3 a is known [3 a is unknown [3 the distribution of volumes is uniform [j the distribution of volumes is normal (c) Interpret your results in the context of this problem. 0 The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. Q We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval. 0 The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. 0 We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval. (CI) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.10 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) :] male firefighters