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The properties of a normal distribution

The properties of a normal distribution. The area under the curve = 1. (x = μ). A local maximum exists at x = μ. The x axis is asymptotic. i.e. the x axis gets closer and closer to the curve but does not touch it. The curve is symmetrical about the mean. Area under the curve = 0.5.

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The properties of a normal distribution

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  1. The properties of a normal distribution

  2. The area under the curve = 1

  3. (x = μ) A local maximum exists at x = μ

  4. The x axis is asymptotic i.e. the x axis gets closer and closer to the curve but does not touch it.

  5. The curve is symmetrical about the mean Area under the curve = 0.5 Area under the curve = 0.5

  6. μ± σ gives us 68 % of the area of the curve i.e. 68 % of its values lie between μ - σ and μ + σ.

  7. μ± 2σ gives us 95 % of the area of the curve i.e. 95 % of its values lie between μ - 2σ and μ + 2σ.

  8. μ± 3σ gives us 99.7 % of the area of the curve i.e. 99.7 % of its values lie between μ - 3σ and μ + 3σ.

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