# The Normal Distribution

The normal (Gaussian) distribution is a probability distribution with a bell-shaped curve that is symmetric about the mean (the average) and has a finite variance (skewed to the right). The normal distribution is useful because it summarizes a large class of probability distributions and is useful in the calculations of probability and statistical measures such as correlation. The normal distribution is so named because it is "normal" or "typical". The normal distribution is used to model the distribution of many variables, including spatial, financial, biological, and other variables. The normal distribution is often used to model random variables which are subject to the same rules (such as selection and independence) as the events of interest in the field under study, but are not necessarily random, such as the heights and weights of people. The normal distribution is often used in the natural and social sciences to represent random variables with a bell-shaped or symmetric distribution, such as the distribution of heights of men and women, the distribution of test scores, or the number of households in a city. The normal distribution is frequently used in statistics for representing variables for which the distribution of values is not known, but for which the mean and standard deviation are known. The normal distribution is also used to model and predict the distribution of many other variables, such as the distribution of the errors in a sample of data, the distribution of the errors in a population, or the distributions of many genetic traits such as blood pressure and body weight. The normal distribution is sometimes used to model the distribution of errors in a sample of data. The normal distribution can be thought of as the best-fitting distribution for a given sample of a given size. If the distribution of a sample of data is normally distributed, it can be concluded that the variables being measured are normally distributed, as well. If a sample of data is not normally distributed, but the distribution of some other variable being measured has a normal distribution, the data can be said to be normally distributed with respect to that variable. This is a more rigorous way to say that the sample is "normally distributed". In addition to describing the distribution of data values, the normal distribution is also used to describe the distribution of errors in a population. The normal distribution is often used to describe the distribution of the errors in a sample of data. If a sample of data has a normal distribution, it can be said to be normally distributed with respect to the whole population. The normal distribution is also used to describe the distributions of many other variables, such as the distribution of the heights of men and women, the distribution of test scores, or the distribution of many genetic traits such as blood pressure and body weight. The normal distribution is used to model the distribution of many biological variables because its mathematical form concisely describes many important biological phenomena. The use of the normal distribution to describe biological variables is not always appropriate, but it is often appropriate. The normal distribution is used as a model to represent the observed distributions of many random variables. The use of the normal distribution to represent the distributions of random variables is not always appropriate, but it is often appropriate. The normal distribution is used as a model to represent the distribution of the heights of men and women, the distribution of test scores, the distribution of the number of households in a city, the distribution of the number of errors in a sample of data, the distribution of the number of houses in a city, and the distribution of the number of cases in a sample of data. The normal distribution is used to model the distribution of many variables because it is the best-fitting distribution for a given sample of a given size. If the distribution of a sample of data is normally distributed, it can be concluded that the variables being measured are normally distributed, as well. If a sample of data is not normally distributed, but the distribution of some other variable being measured has a normal distribution, the data can be said to be normally distributed with respect to that variable. This is a more rigorous way to say that the sample is "normally distributed". In addition to describing the distribution of data values, the normal distribution is also used to describe the distribution of errors in a population. The normal distribution is often used to describe the distribution of the errors in a sample of data. If a sample of data has a normal distribution, it can be said to be normally distributed with respect to the whole population. The normal distribution is also used to describe the distributions of the errors in a sample of data. If a sample of data has a normal distribution, it can be said to be normally distributed with respect to the whole population. The normal distribution is used to model the distribution of many variables because it is the best-fitting distribution for a given sample of a given size. If the distribution of a sample of data is normally distributed, it can be concluded that the variables being