Normal Distribution

The normal distribution, also known as the Gaussian distribution, is a continuous Probability Distribution that describes the probability of a variable occurring within a specific range of values. It is characterized by its symmetrical bell-shaped curve, with the center point representing the most likely value and the tails tapering off towards negative and positive infinity.


Notes:

  • Probability Density Function (PDF): It describes the relative likelihood of a specific value occurring. The PDF is highest at the center (mean) and gradually decreases towards the tails.
  • Parameters: The normal distribution is fully defined by two parameters:
    • Mean: The average value of the distribution, representing the center of the symmetrical bell curve.
    • Standard Deviation: A measure of spread in the data. A larger standard deviation indicates a wider bell curve with more data points further from the mean.
  • Empirical Rule (68-95-99.7 Rule): This rule states that for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations of the mean.
  • Central Limit Theorem: This fundamental theorem in statistics states that the sum of a large number of independent random variables, even if they are not normally distributed, tends towards a normal distribution as the number of variables increases.
  • Normal Distribution serves as a foundation for Hypothesis Testing, Confidence Interval, and many statistical analyses.