Formula Review

Introduction

XN(μ, σ)

μ = the mean; σ = the standard deviation

6.1 The Standard Normal Distribution

Z ~ N(0, 1)

z = a standardized value (z-score)

mean = 0; standard deviation = 1

To find the kth percentile of X when the z-score is known,


 
k = μ + (z)σ

z-score: z = x – μσx – μσ

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)