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

Question:

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. 68.26% of all possible samples have means that lie within of the population mean, μ.
b. 95.44% of all possible samples have means that lie within of the population mean, μ.
c. 99.74% 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.