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The chi‐squared distribution (or χ²‐distribution) with n degrees of freedom (Figure 4.14b) is the distribution of a sum of the squares of n independent standard Normal random variables. The chi‐squared distribution is always positive and its shape is uniquely determined by the degrees of freedom. The distribution becomes more symmetrical as the degrees of freedom increase and when the degrees of freedom are greater than 50, the chi‐squared distribution is very similar to the Normal distribution. The chi‐squared distribution is used in the common chi‐squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a Normal distribution from a sample standard deviation.