## 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: \(Z \sim N(0, 1)\).