Answer:
As the degrees of freedom increase, the shape of the chi-square distribution becomes more symmetrical and approaches a normal distribution. Specifically, the chi-square distribution becomes more bell-shaped and less skewed as the degrees of freedom increase.
For example, when the degrees of freedom are small (e.g., less than 10), the chi-square distribution is highly skewed to the right, with a long tail extending to the right. However, as the degrees of freedom increase, the skewness decreases and the distribution becomes more symmetric.
Furthermore, as the degrees of freedom increase, the peak of the distribution moves to the right, and the spread of the distribution becomes narrower. Specifically, the standard deviation of the chi-square distribution decreases as the degrees of freedom increase, which means that the distribution becomes less variable and more tightly clustered around its mean.