A variable of a population is normally distributed with mean and standard deviation . For samples

A variable of a population is normally distributed with mean μ

and standard deviation σ. For samples of size n, fill in the blanks.

Justify your answers.

a. Approximately 68% of all possible samples have means that lie within of the population mean, μ.

b. Approximately 95% of all possible samples have means that lie within of the population mean, μ.

c. Approximately 99.7% of all possible samples have means that lie within of the population mean, μ.

d. 100(1 − α)% of all possible samples have means that lie within of the population mean, μ. (Hint: Draw a graph for the distribution of x¯, and determine the z-scores dividing the area under the normal curve into a middle 1 − α area and two outside areas of α/2.)