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 of 42 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that = 7.80 ml/kg for the distribution of blood plasma.
(a)
Find the margin of error for a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Round your answer to two decimal places.)
3.10

Correct: Your answer is correct.
ml/kg
Find a 99% confidence interval for the population mean blood plasma volume (in ml/kg) in male firefighters. (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.)

Incorrect: Your answer is incorrect.
ml/kg
(b)
What conditions are necessary for your calculations? (Select all that apply.)
is unknown
is known
the distribution of volumes is normal
the distribution of volumes is uniform
n is large

(c)
Interpret your results in the context of this problem.
We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.
The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.
The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
(d)
Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
male firefighters