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 of47male 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=7.00ml/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 limitupper limitmargin of error

(b) What conditions are necessary for your calculations? (Select all that apply.)

nis large

the distribution of weights is normal

is known

is unknown

the distribution of weights is uniform