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 = 7.70ml/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.)
σ is known
σ is unknown
the distribution of weights is uniform
n is large
the distribution of weights is normal
(c) Interpret your results in the context of this problem.
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 is0.99.  Â
1% 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.
(d) Find the sample size necessary for a 99% confidence level withmaximal margin of error E = 3.00 for the mean plasmavolume in male firefighters. (Round up to the nearest wholenumber.)
