4.5: Chapter 4 Formula Review
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- 50561
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Introduction
\(X \sim N(\mu, \sigma)\)
\(\mu =\) the mean; \(\sigma =\) the standard deviation
4.1 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
\(Z \sim N(0, 1)\)
4.3 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: \(Z \sim N(0, 1)\).