Key Terms

Normal Distribution

a continuous random variable (RV) with pdf f(x) = $\frac{1}{\sigma \sqrt{2\pi }}{\text{ e}}^{{\frac{–(x–\mu )}{2{\sigma }^2}}^2}$, 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 RV is called the standard normal distribution.

Standard Normal Distribution

a continuous random variable (RV) X ~ N(0, 1); when X follows the standard normal distribution, it is often noted as Z ~ N(0, 1).

z-score

the linear transformation of the form z = $\frac{x–\mu }{\sigma }$; if this transformation is applied to any normal distribution X ~ N(μ, σ) the result is the standard normal distribution Z ~ N(0,1). If this transformation is applied to any specific value x of the RV with mean μ and standard deviation σ, the result is called the z-score of x. The z-score allows us to compare data that are normally distributed but scaled differently.