X ∼ N(μ, σ)

μ = the mean; σ = the standard deviation

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 = $\frac{x\text{ – }\mu }{\sigma }$

Z = the random variable for z-scores

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

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

Calculator function for probability: normalcdf (lower x value of the area, upper x value of the area, mean, standard deviation)

Calculator function for the k^th percentile: k = invNorm (area to the left of k, mean, standard deviation)