The expression for normal distribution is given by the probability density function (PDF) of the normal distribution, which is:
f(x) = (1/√(2πσ^2)) * e^(-1/2((x-μ)/σ)^2)
μ represents the mean or average of the distribution. It is the center point of the curve and indicates the most probable value.
σ represents the standard deviation of the distribution. It measures how spread out the data is from the mean. A smaller σ indicates a narrower curve and a larger σ indicates a wider curve.
Normal distribution is commonly used in statistics to model and analyze continuous data. It is used to calculate probabilities and make predictions about a population based on a sample. It is also used in hypothesis testing and to determine confidence intervals.
The 68-95-99.7 rule is a commonly used rule of thumb in normal distribution. It states that approximately 68% of the data falls within one standard deviation (σ) of the mean (μ), 95% falls within two σ of the mean, and 99.7% falls within three σ of the mean. This rule is also known as the empirical rule or the 3-sigma rule.