X ∼ N(μ, σ)

μ = the mean; σ = the standard deviation

Z ~ N(0, 1)

z = a standardized value (z-score)

mean = 0; standard deviation = 1

To find the observed value, x, when the z-scores is known:
x = μ + (z)σ

z-score: z = $\frac{x\text{ – }\mu }{\sigma }$ or z = $\frac{|x–\mu |}{\sigma }$

Z = the random variable for z-scores

Z ~ N(0, 1)

Normal Distribution: X ~ N(µ, σ) where µ is the mean and σ is the standard deviation.

Standard Normal Distribution: Z ~ N(0, 1).