Total plasma volume is important in determining the required plasma component in

Question

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 50 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 = 8.00 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.)

lower limit=

upper limit=

margin of error=

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

n is large

the distribution of weights is uniform

is known

the distribution of weights is normal

is unknown

(c) 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

Explanation / Answer

here std error =std deviation/(n)1/2 =1.1314

for 99% CI. z=2.5758

hence margin of error =z*std error =2.9142

hence lower limit =x-margin of error =34.5858

upper limit =x+ margin of error =40.4142

b)

is known

the distribution of weights is normal

c) for sample size =(z*std deviation/E)2 =~48

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