What Normal distrib is
Normal distribution (also known as the Gaussian distribution) is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is a continuous probability distribution described by its mean and standard deviation, which is determined by the spread of the data. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
Steps for Normal Distribution:
- Determine the mean (μ) and standard deviation (σ).
- Draw a graph of the normal distribution by plotting the data points.
- Calculate the area under the curve.
- Determine the probability of a value occurring between two points of the curve.
- Calculate the z-score of a value to determine its position on the curve.
- Use the area under the curve to determine the probability of a value falling below or above the mean.
Examples
- In finance, normal distributions are used to model stock returns.
- In medicine, normal distributions are used to calculate the probability of a drug having a certain side effect.
- In engineering, normal distributions are used to model the reliability of a product.
- In psychology, normal distributions are used to measure the intelligence of a population.
- In education, normal distributions are used to measure the academic performance of students.
- In sports, normal distributions are used to measure the performance of athletes.
- In manufacturing, normal distributions are used to model production yields and quality control.
- In meteorology, normal distributions are used to model the probability of extreme weather events.