Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person

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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 41 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 𝜎 = 7.70 ml/kg for 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.)
(b) What conditions are necessary for your calculations? (Select
all that apply.)
𝜎 is unknownn is largethe distribution of
volumes is normalthe distribution of volumes is uniform𝜎 is
known
(c) Interpret your results in the context of this problem.
The probability that this interval contains the true average
blood plasma volume in male firefighters is 0.01.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 0.99.
(d) Find the sample size necessary for a 99% confidence level with
maximal margin of error E = 2.20 for
the mean plasma volume in male firefighters. (Round up to the
nearest whole number.)
male firefighters