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Statistics LibreTexts

6.4: Chapter Formula Review

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  • 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: \(Z \sim N(0, 1)\).

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