X ∼ N(μ, σ)
μ = the mean; σ = the standard deviation
6.1 The Standard Normal Distribution
z = a standardized value (z-score)
mean = 0; standard deviation = 1
To find the kth percentile of X when the z-scores is known:
k = μ + (z)σ
z-score: z =
Z = the random variable for z-scores
6.2 Using the Normal Distribution
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 kth percentile: k = invNorm (area to the left of k, mean, standard deviation)