The Normal Distribution and the Empirical Rule (Leaving Cert Mathematics): Flashcards

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The Normal Distribution and the Empirical Rule
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When does normal distribution appear?

Large groups: physical characteristics (height, weight)

Shape of normal distribution

Bell-shaped and symmetrical

Another name for normal curve

Curve of normal distribution

Symbol for standard deviation

σ\sigma

What σ\sigma measures

Spread of data from the mean

% within one standard deviation

68%

% within two standard deviations

95%

% within three standard deviations

99.7%

68% range formula

[xˉ−σ,xˉ+σ][\bar{x} - \sigma, \bar{x} + \sigma]

95% range formula

[xˉ−2σ,xˉ+2σ][\bar{x} - 2\sigma, \bar{x} + 2\sigma]

99.7% range formula

[xˉ−3σ,xˉ+3σ][\bar{x} - 3\sigma, \bar{x} + 3\sigma]

Key percentages to remember (Empirical Rule)

68-95-99.7

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