Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of41male firefighters are tested and that they have a plasma volume sample mean ofx= 37.5 ml/kg(milliliters plasma per kilogram body weight). Assume that=8.00ml/kgfor the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma 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? (Select all that apply.)

• the distribution of volumes is normal
• nis large
• is known
• is unknown
• the distribution of volumes is uniform

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

• 1. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
• 2. We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
• 3. We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.
• 4. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of errorE=2.70for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

• _______male firefighters