The normal Gaussian distribution, commonly referred to as the normal distribution, is a fundamental concept in statistics and probability theory. It is characterized by its bell-shaped curve, which is symmetric around the mean, indicating that most observations cluster around this central value. The normal distribution is defined by its mean and standard deviation, with the mean, median, and mode all being equal. This distribution is significant due to the Central Limit Theorem, which states that the sum of independent random variables tends toward a normal distribution, regardless of the original distributions of the variables involved.