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Total plasma volume is important in determining the requiredplasma component in blood replacement therapy for a personundergoing surgery. Plasma volume is influenced by the overallhealth and physical activity of an individual. Suppose that arandom sample of 46 male firefighters are tested and that they havea plasma volume sample mean of x = 37.5 ml/kg (milliliters plasmaper kilogram body weight). Assume that ? = 7.50 ml/kg for thedistribution of blood plasma. (a) Find a 99% confidence intervalfor the population mean blood plasma volume in male firefighters.What is the margin of error? (Round your answers to two decimalplaces.) lower limit upper limit margin of error (b) Whatconditions are necessary for your calculations? (Select all thatapply.) the distribution of weights is normal the distribution ofweights is uniform ? is unknown n is large ? is known (c) Interpretyour results in the context of this problem. 1% of the intervalscreated using this method will contain the true average bloodplasma volume in male firefighters. The probability that thisinterval contains the true average blood plasma volume in malefirefighters is 0.01. 99% of the intervals created using thismethod will contain the true average blood plasma volume in malefirefighters. The probability that this interval contains the trueaverage blood plasma volume in male firefighters is 0.99. (d) Findthe sample size necessary for a 99% confidence level with maximalmargin of error E = 2.80 for the mean plasma volume in malefirefighters. (Round up to the nearest whole number.) malefirefighters