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 50 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.)

σ is knownthe distribution of weights isuniformn is largethe distribution of weights isnormalσ is unknown

(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.99% of theintervals created using this method will contain the true averageblood plasma volume in malefirefighters.     The probability thatthis interval contains the true average blood plasma volume in malefirefighters is 0.99.The probability that this interval containsthe true average blood plasma volume in male firefighters is0.01.

(d)

Find the sample size necessary for a 99% confidence level withmaximal margin of error E = 2.20 for the mean plasmavolume in male firefighters. (Round up to the nearest wholenumber.)

male firefighters