Normal Distribution 1
Normal Distribution Normal Distribution Author: Dr. Brajesh Kumar Jha Introduction The Normal Distribution (also known as the Gaussian Distribution ) is a continuous probability distribution that describes data clustering around a mean value in a symmetric, bell-shaped curve. It is widely used in statistics, science, and engineering to model real-world phenomena such as heights, weights, IQ, and measurement errors. Definition and Formula A random variable X is said to follow a Normal Distribution with mean μ and standard deviation σ if: \f(x)=(1/(σ√(2π)))*e^(-½((x-μ)/σ)²), -∞ < x < ∞ μ = Mean (center of the curve) σ = Standard Deviation (spread) Total area under the curve = 1 Normal Distribution Curve Properties of Normal Distribution Bell-shaped and symmetric about the mean. Mean = Median = Mode. Total area under the curve is 1. 68.26% of data lies within μ ± σ. 95.44% within μ ± 2σ. 99.73% within μ ± 3σ. Curve is asymptotic to the ...
