A normal distribution, also known as a Gaussian distribution, is a probability distribution that is symmetric around its mean, meaning that the data is equally likely to fall on either side of the mean. It is a fundamental concept in statistics and probability theory, playing a crucial role in various scientific and mathematical fields. Here’s a comprehensive overview of the normal distribution:

# 1. Characteristics of the Normal Distribution:

## a. Symmetry:

- The normal distribution is symmetric, meaning that if you were to draw a vertical line at the mean, the two halves of the distribution would mirror each other.

## b. Bell-Shaped Curve:

- The graph of a normal distribution forms a bell-shaped curve, with the highest point at the mean.

## c. Measures of Central Tendency:

- The mean, median, and mode are all equal in a perfectly normal distribution.

## d. Standard Deviation:

- The spread or dispersion of the distribution is determined by the standard deviation. About 68% of the data falls within one standard deviation of the mean, 95% within two standard…