$\overline{�}$. If the size (n) of the sample is sufficiently large, then X–

$\overline{�}$ ~ N(μ, σn√

$\frac{�}{\sqrt{�}}$). If the size (n) of the sample is sufficiently large, then the distribution of the sample means will approximate a normal distributions regardless of the shape of the population. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, σn√

$\frac{�}{\sqrt{�}}$, is called the standard error of the mean.

$\overline{�}$) is x¯ = Sum of all values in the sampleNumber of values in the sample

$\overline{�}\text{ = }\frac{\text{Sum of all values in the sample}}{\text{Number of values in the sample}}$, and the mean for a population (denoted by μ) is μ = Sum of all values in the populationNumber of values in the population

$�\text{ = }\frac{\text{Sum of all values in the population}}{\text{Number of values in the population}}$.

$�(�)\text{ = }\frac{1}{�\sqrt{2�}} {�}^{\frac{–{\text{(}�–�)}^2}{2{�}^2}}$, where μ is the mean of the distribution and σ is the standard deviation.; notation: X ~ N(μ, σ). If μ = 0 and σ = 1, the random variable, Z, is called the standard normal distribution.

$\frac{�}{\sqrt{�}}$.