Normal Distribution
The normal distribution, also known as the Gaussian distribution, is characterised by its bell-shaped curve and relevance towards applied mathematics. It is important as it is the outcome of a probabilistic event with finite mean and variance provided that it is repeated infinitely.
Properties of the Normal Distribution
- Symmetry: The normal distribution is perfectly symmetrical around its mean (μ).
- Mean, Median, and Mode: In a normal distribution, the mean, median, and mode are all equal.
- Continuous Distribution: The normal distribution is a continuous probability distribution.
- Asymptotic Behavior: The tails of the distribution extend infinitely in both directions, approaching but never touching the x-axis.
The normal distribution is often referred to as the "bell curve" due to its characteristic shape.
Graph Representation
The normal distribution curve is as a smooth, symmetrical bell-shaped curve. The highest point of the curve corresponds to the mean (μ), which is also the median and mode of the distribution. The spread of the curve is determined by the standard deviation (σ).
When sketching a normal distribution curve, remember that it should be symmetrical and that the tails should never completely touch the x-axis.
Natural Occurrence
Normal distributions are ubiquitous in nature and human-related phenomena. Some examples include:
- Heights of individuals in a population
