# 4.5: Chapter 6 Formula Review

## Introduction

$$X \sim N(\mu, \sigma)$$

$$\mu =$$ the mean; $$\sigma =$$ the standard deviation

## The Standard Normal Distribution

$$Z \sim N(0, 1)$$

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

mean = 0; standard deviation = 1

To find the $$k^{\text{th}}$$ percentile of $$X$$ when the z-scores is known:
$$k = \mu + (z)\sigma$$

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

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

$$Z \sim N(0, 1)$$

## Estimating the Binomial with the Normal Distribution

Normal Distribution: $$X \sim N(\mu, \sigma)$$ where $$\mu$$ is the mean and $$\sigma$$ is the standard deviation.

Standard Normal Distribution: $$Z \sim N(0, 1)$$.