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 47 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 = 7.80ml/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 ___ Â

(b) What conditions are necessary for your calculations? (Selectall that apply.)

σ is unknown

the distribution of weights is uniform

the distribution of weights is normal

n is large

σ is known

(c) Interpret your results in the context of this problem.

1% of the intervals created using this method will contain thetrue average blood plasma volume in male firefighters.Theprobability that this interval contains the true average bloodplasma volume in male firefighters is0.01.    99% of the intervals created usingthis method will contain the true average blood plasma volume inmale firefighters.The probability that this interval contains thetrue average blood plasma volume in male firefighters is 0.99.

(d) Find the sample size necessary for a 99% confidence level withmaximal margin of error E = 2.90 for the mean plasmavolume in male firefighters. (Round up to the nearest wholenumber.)
male firefighters