What defines a normal distribution in statistics?

• A. A normal distribution is asymmetric.
• B. A normal distribution is a probability distribution symmetrical about the mean.
• C. A normal distribution has multiple peaks.
• D. A normal distribution has a definitive maximum value.

Answer: (B)

A normal distribution is defined as a probability distribution that is perfectly symmetrical about the mean, meaning that the data is arranged in such a way that the left and right sides of the distribution are mirror images of each other. This symmetry implies that the mean, median, and mode of the distribution are all equal and located at the center of the distribution.

In a normal distribution, most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally on both sides. This characteristic shape is often referred to as a "bell curve" due to its resemblance to a bell. The area under the curve represents the total probability and is equal to 1, with about 68% of the data falling within one standard deviation of the mean, approximately 95% within two standard deviations, and about 99.7% within three standard deviations, known as the empirical rule.

In contrast to this, a normal distribution is not asymmetrical, does not feature multiple peaks (which would indicate a multimodal distribution), and does not have a definitive maximum value, as it theoretically extends infinitely in both directions along the x-axis. Thus, the definition captured in the correct choice reflects the essential properties of a normal distribution.