Normal distribution – standard normal distribution

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NEET PG High-Yield: Normal Distribution

The Normal (Gaussian) distribution is the most important probability distribution in statistics, characterized by a symmetrical, bell-shaped curve.

Key Characteristics

Feature Description
Symmetry Mean = Median = Mode coincide at the center.
Asymptotic The tails approach the horizontal axis but never touch it.
Total Area The total area under the curve is exactly **1 (or 100%)**.
High-Yield NEET PG Pearls:

  • The 68-95-99 Rule:

    • ± 1 SD: 68.27% of data

    • ± 1.96 SD: 95% of data

    • ± 2.58 SD: 99% of data

    • ± 3 SD: 99.73% of data

  • Standard Normal Distribution: A special case where the Mean = 0 and the standard deviation = 1.
  • Z-Score: Defined as Z = (x - mu) / sigma. It measures how many standard deviations a value (x) is from the mean (mu).
  • Importance: Most parametric statistical tests (t-test, ANOVA) assume the underlying data follow a normal distribution.