What does the standard deviation determine about the normal curve?

The standard deviation in a normal distribution is a critical measure that primarily assesses the variability of the data. It quantifies how close the data points are to the mean (center point) of the distribution. A smaller standard deviation indicates that the data points tend to be closer to the mean, leading to a steeper curve, while a larger standard deviation suggests that the data points are more spread out, resulting in a flatter curve.

Thus, the correct understanding is that the standard deviation plays a pivotal role in determining the shape of the normal curve, particularly its width. It does not define the center point or the total area under the curve; instead, those aspects are represented by the mean and the properties of the normal distribution, respectively.