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 of50male firefighters are tested and that they have a plasma volume sample mean ofx=32.1ml/kg(milliliters plasma per kilogram body weight). Assume that=7.40ml/kgfor the distribution of blood plasma.

When finding an98% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)

z_c=

(a)Find a98% 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.)

the distribution of weights is uniform

nis large

the distribution of weights is normal

is known

is unknown

(c)Interpret your results in the context of this problem.

We are 2% 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 0.98.

We are 98% 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 0.02.

(d)Which equation is used to find the sample sizenfor estimatingwhenis known?

Find the minimal sample size necessary for a98% confidence level with maximal margin of errorE=2.50for the mean plasma volume in male firefighters. (Round your answer to a whole number.)