Sections

Key Terms
# 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*= $\frac{x\text{}\u2013\text{}\mu}{\sigma}$; 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.