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 41 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 = 8.00ml/kg for the distribution of blood plasma.
(a) Find a 99% confidence interval for the population mean bloodplasma volume in male firefighters. What is the margin of error?(Round your answers to two decimal places.)
| lower limit    | |
| upper limit    | |
| margin of error    | |
(b) What conditions are necessary for your calculations? (Selectall that apply.)
n is largethe distribution of weights isnormalσ is unknownσ is knownthe distribution ofweights is uniform
(c) Interpret your results in the context of this problem.
The probability that this interval contains the true averageblood plasma volume in male firefighters is 0.01.We are 1%confident that the true average blood plasma volume in malefirefighters falls within thisinterval.     The probability that thisinterval contains the true average blood plasma volume in malefirefighters is 0.99.We are 99% confident that the true averageblood plasma volume in male firefighters falls within thisinterval.
(d) Find the sample size necessary for a 99% confidence level withmaximal margin of error E = 2.40 for the mean plasmavolume in male firefighters. (Round up to the nearest wholenumber.)
male firefighters
