Key Terms

normal distribution
a continuous random variable (RV) 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 = x  μσx  μσ; 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.