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1.10 The Normal Distribution

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The Normal Distribution

The normal distribution

Key properties:

  • Bell-shaped and symmetric about the mean μ{\mu}
  • Mean = Median = Mode (all at the center)
  • Extends infinitely in both directions
  • Total area under the curve = 1 (represents 100% of data)
  • Notation: X∼N(μ,σ){X \sim N(\mu, \sigma)}
The Empirical Rule (68-95-99.7 rule):
P(μ−σ<X<μ+σ)≈0.68P(\mu - \sigma < X < \mu + \sigma) \approx 0.68
P(μ−2σ<X<μ+2σ)≈0.95P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 0.95
P(μ−3σ<X<μ+3σ)≈0.997P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 0.997

If heights are N(170,8){N(170, 8)}: 68% of heights are between 162 and 178 cm.

In this unit

10 lessons

  1. 1.1Introducing Statistics: What Can We Learn from Data?Preview lesson
  2. 1.2The Language of Variation: VariablesPreview lesson
  3. 1.3Representing a Categorical Variable with TablesPreview lesson
  4. 1.4Representing a Categorical Variable with GraphsPreview lesson
  5. 1.5Representing a Quantitative Variable with GraphsPreview lesson
  6. 1.6Describing the Distribution of a Quantitative VariablePreview lesson
  7. 1.7Summary Statistics for a Quantitative VariablePreview lesson
  8. 1.8Graphical Representations of Summary StatisticsPreview lesson
  9. 1.9Comparing Distributions of a Quantitative VariablePreview lesson
  10. 1.10The Normal DistributionThis lesson

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