# Question: A variable of a population is normally distributed with mean

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.

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.

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