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 44 male firefighters are tested and that they havea plasma volume sample mean of x = 37.5 ml/kg (millilitersplasma per kilogram body weight). Assume that σ = 7.60ml/kg for the distribution of blood plasma.
(a) Find a 99% confidence interval for the populationmean blood plasma volume in male firefighters. What is the marginof error? (Round your answers to two decimal places.)
| lower limit    | |
| upper limit    | |
| margin of error |
(b) What conditions are necessary for your calculations?(Select all that apply.)
-σ is unknown
-n is large
-the distribution of weights is normal
-σ is known
-the distribution of weights is uniform
(c) Interpret your results in the context of thisproblem.
-99% of the intervals created using this method will contain thetrue average blood plasma volume in male firefighters.
-The probability that this interval contains the true averageblood plasma volume in male firefighters is 0.01.
-The probability that this interval contains the true averageblood plasma volume in male firefighters is 0.99.
-1% of the intervals created using this method will contain thetrue average blood plasma volume in male firefighters.
(d) Find the sample size necessary for a 99% confidencelevel with maximal margin of error E = 2.50 for the meanplasma volume in male firefighters. (Round up to the nearest wholenumber.)
_________ male firefighters
