Definition:

The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution characterized by its symmetric bell-shaped curve.

Characteristics:

• Shape: The distribution has a bell-shaped curve that is symmetric around the mean.
• Mean and Median: The mean and median of the distribution are equal and located at the center of the curve.
• Standard Deviation: The spread of the distribution is determined by the standard deviation. A smaller standard deviation results in a narrower curve, while a larger standard deviation produces a wider curve.
• 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.
• Z-Score: Z-score is a measure of how many standard deviations a particular value is from the mean. It helps in comparing values from different normal distributions.

Applications:

The normal distribution is widely used in various fields due to its ubiquity in natural phenomena and its mathematical properties. Some common applications include:

• Economics: In financial markets, stock prices, and economic indicators often follow a normal distribution.
• Statistics: Normal distribution serves as a foundation for many statistical models and hypothesis tests.
• Quality Control: It is used for process control and monitoring in manufacturing industries.
• Psychology: Human characteristics such as IQ scores, heights, and weights tend to exhibit a normal distribution.

Overall, the normal distribution is a fundamental concept in statistics and serves as a useful model for various random phenomena.