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 (milliliters plasmaper kilogram body weight). Assume that σ = 7.20 ml/kg for thedistribution 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 unknown

-n is large

-the distribution of weights is uniform

-the distribution of weights is normal σ is known

(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.

-1% of the intervals created using this method will contain thetrue average blood plasma volume in male firefighters.

-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 is 0.01.

(d) Find the sample size necessary for a 99% confidence levelwith maximal margin of error E = 2.30 for the mean plasma volume inmale firefighters. (Round up to the nearest whole number.) malefirefighters