6.7: Formula Review

6.1 Introduction

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

\(\mu=\) the mean; \(\sigma=\) the standard deviation

6.2 The Standard Normal Distribution

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

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

mean \(=0\); standard deviation \(=1\)

To find the observed value, \(x\), when the \(z\)-scores is known:
\(x=\mu+(z) \sigma\)

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

\(Z=\) the random variable for \(z\)-scores

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

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