What type of distribution would you expect if the data peaks around the center with symmetrical tails?

The description of the data peaks around the center with symmetrical tails aligns perfectly with the characteristics of a normal distribution. In a normal distribution, the data is symmetrically distributed around the mean, meaning that most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off symmetrically in both directions.

This bell-shaped curve is a defining feature of normal distributions, where about 68% of the data falls within one standard deviation of the mean, and about 95% falls within two standard deviations. The symmetry is crucial; it indicates that the left half of the distribution mirrors the right half, leading to equal tail lengths and widths.

In contrast, uniform distributions exhibit a constant frequency across a range, showing no peak or symmetry. Skewed distributions, whether left or right, display asymmetry in their shape, making them not fit the description provided. Bimodal distributions have two distinct peaks, which sharply contrasts the central peak described in the question. Therefore, the normal distribution is the only appropriate choice given the provided characteristics.