A normal distribution, also known as a Gaussian distribution, is a type of continuous probability distribution for a real-valued random variable. It is symmetrical around its mean, and most of the observations cluster around the central peak, with the probabilities for values further away from the mean tapering off equally in both directions. The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Some key features of the normal distribution include:

• Bell-shaped curve: The normal distribution has a bell-shaped curve, with the highest point at the mean and tapering off equally in both directions.

• Mean and standard deviation: The mean of a normal distribution is zero, and the standard deviation is one.

• Symmetry: The normal distribution is symmetric around its mean.

• Empirical rule: The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

The normal distribution is important because it accurately describes the distribution of values for many natural phenomena, such as heights, blood pressure, measurement error, and IQ scores. It is also important because it can be used to approximate other types of probability distributions, such as binomial, hypergeometric, and negative.