statistic question

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 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 𝜎 = 7.20 ml/kg for the distribution of blood plasma.

Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.40 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

Answer 1

n = (z* S/E)^2 = (2.575 * 7.2/2.4)^2 = 59.676 ~ 60