The normal distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics to model continuous random variables that have a bell-shaped probability density function. It is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean represents the center of the distribution, and the standard deviation represents the spread or variability of the data.

The probability density function of the normal distribution is given by:

f(x) = (1/σ√(2π)) * e^(-1/2((x-μ)/σ)^2)

where e is the base of the natural logarithm, and π is the mathematical constant pi.

The normal distribution has several important properties, such as:

1. It is a symmetric distribution, with the mean, median, and mode all equal to each other.
2. The total area under the curve of the normal distribution is equal to 1.
3. The standard normal distribution, which has a mean of 0 and a standard deviation of 1, is often used as a standard for comparison with other normal distributions.
4. Many real-world phenomena, such as height and weight measurements, follow a normal distribution.
5. The central limit theorem states that, under certain conditions, the sum or average of a large number of independent and identically distributed random variables will have a normal distribution.