Normal distribution, the most common distribution function for independent, randomly generated variables. Its familiar bell-shaped curve is ubiquitous in statistical reports, from survey analysis and quality control to resource allocation. Learn more about normal distribution in this article. Properties of the Normal Distribution The Empirical Rule. For all normal distributions, 68.2% of the observations will appear within plus or minus one Skewness. Skewness measures the degree of symmetry of a distribution. The normal distribution is symmetric and has a Kurtosis. Kurtosis The normal distribution model always describes a symmetric, unimodal, bell shaped curve. However, these curves can look different depending on the details of the model. Specifically, the normal distribution model can be adjusted using two parameters: mean and standard deviation. Normal distributions come up time and time again in statistics. A normal distribution has some interesting properties: it has a bell shape, the mean and median are equal, and 68% of the data falls within 1 standard deviation. What is a normal distribution? Normal distributions are symmetric around their mean. The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0 1.0. Normal distributions are denser in the center and less dense in the tails. Normal distributions are defined by two parameters, the mean (μ μ) and the standard deviation (σ σ ). Normal distributions can differ in their means and in their standard deviations. Figure 4.5.1 4.5. 1 shows three normal distributions. The green (left-most) distribution has a mean of -3 and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the distribution in black A normal distribution, sometimes called the bell curve (or De Moivre distribution [1]), is a distribution that occurs naturally in many situations. For example, the bell curve is seen in tests like the SAT and GRE. Vi5mp58.