In a normal distribution, what aspect fundamentally characterizes its shape?

A normal distribution is fundamentally characterized by its symmetrical shape around the mean. This means that the distribution is evenly balanced, with equal proportions of data points falling on either side of the mean. This symmetry is a core property of the normal distribution, which leads to the familiar bell-shaped curve. The highest point of the curve corresponds to the mean, median, and mode, all of which coincide in a perfectly normal distribution.

In addition to its symmetry, the normal distribution also has specific probabilities associated with standard deviations from the mean, where about 68% of the data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations. This characteristic is crucial for many statistical methods, as it allows for the application of various statistical techniques and inferences.

The other options presented do not accurately characterize the normal distribution. The presence of a peak at both tails would suggest a different type of distribution, positively skewed distributions do not exhibit symmetry, and a linear relationship between values is not a defining feature of the distribution's shape but rather pertains to correlations or regression analyses.