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

Question

Total plasma volume is important in determining the required component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Previous studies indicate that the standard deviation of the distribution of blood plasma volume for male firefighters within 2.50ml/kg of the population mean, . How m plasma was 7.50ml/kg. A physician wants to estimate the population mean any male firefighters should be included in the sample to be 95% confident that the sample mean plasma volume, F is within the given margin of error.

Explanation / Answer

The population mean plasma volume should be estimated within 2.5 ml/kg of the population mean for male fire fighters.

So, the length of the confidence interval is = 2*2.5 ml/kg = 5 ml/kg

We know that 95% confidence interval for population mean when population sd is known is given by,

LCL = sample mean - (sd / sqrt(n))* z(alpha/2)

UCL =  sample mean + (sd / sqrt(n))* z(alpha/2) ; z(alpha/2) = upper (alpha/2) point of a standard normal distribution [here, alpha = 0.05, so, z(0.025) = 1.96 and sd = 7.5 ml/kg]

Now it is given that,

(sd /sqrt(n))*z(0.025) = 2.5

which implies, sqrt(n) = sd*z(0.025) / 2.5 = 7.5*1.96 / 2.5 = 3*1.96 = 5.88

Therefore, n = 34.5744 which is approximately equal to 35

Therefore, 35 male fire fighters should be included in the sample.

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