### Introduction

*X* âˆ¼ *N*(*Î¼*, *Ïƒ*)

*Î¼* = the mean;
*Ïƒ* = the standard deviation

### 6.1 The Standard Normal Distribution

*z* = a standardized value (*z*-score)

mean = 0; standard deviation = 1

To find the observed value, *x*, when the *z*-scores is known:*x* = *Î¼* + (*z*)*Ïƒ*

*z*-score: *z* = $\frac{x\text{\xe2\u20ac\u201c}\mathrm{\xce\xbc}}{\mathrm{\xcf\u0192}}$

*Z* = the random variable for *z*-scores

### 6.2 Using the Normal Distribution

Normal Distribution: *X* ~ *N*(*Âµ*, *Ïƒ*) where *Âµ* is the mean and *Ïƒ* 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)