What happens when the standard deviation is larger in a normal distribution?

In a normal distribution, the standard deviation plays a crucial role in determining the shape of the distribution curve. When the standard deviation is larger, this indicates that the data points are more spread out from the mean. As a result, the overall shape of the curve flattens. This flattening is associated with thicker tails, meaning that there are more data points that fall further away from the mean in both directions.

This phenomenon occurs because a larger standard deviation accommodates a wider range of values, reflecting greater variability in the dataset. Thus, the tails of the distribution extend further to both ends, which captures more extreme values. In summary, an increase in standard deviation results in a distribution that is more spread out and has thicker tails. This key characteristic of how standard deviation affects the normal distribution is fundamental in understanding statistical analysis and interpretation.