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 42 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 = 7.20ml/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 limitupper limitmargin of error

(b)

What conditions are necessary for your calculations? (Select allthat apply.)

the distribution of weights is uniformn islargeσ is unknownσ is knownthe distribution ofweights is normal

(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 0.99.99% of theintervals created using this method will contain the true averageblood plasma volume in male firefighters.    1%of the intervals created using this method will contain the trueaverage blood plasma volume in male firefighters.The probabilitythat this interval contains the true average blood plasma volume inmale firefighters is 0.01.

(d)

Find the sample size necessary for a 99% confidence level withmaximal margin of error E = 2.00 for the mean plasmavolume in male firefighters. (Round up to the nearest wholenumber.)

male firefighters