Final answer:
The correct characteristic that describes the normal distribution is option (a) Symmetric and bell-shaped, as it implies symmetry and the mean, median, and mode all being located at the same point on the distribution.
Step-by-step explanation:
The question asks about the characteristics of the normal distribution. Among the options provided, the normal distribution is described by being symmetric and bell-shaped. The characteristics of a normal distribution include it being a symmetrical curve where the mean, median, and mode all coincide at the highest point in the middle of the distribution. This symmetry implies that the left and right halves of the distribution are mirror images of each other. Moreover, the Empirical Rule states that for a normal distribution approximately 68 percent of the data is within one standard deviation of the mean, approximately 95 percent is within two standard deviations, and more than 99 percent is within three standard deviations. This closely links to what is known as Chebyshev's Rule, which has wider applicability regardless of the data distribution shape, and asserts that a certain percentage of data falls within a certain number of standard deviations from the mean (at least 75% within two standard deviations, at least 89% within three, and at least 95% within 4.5 standard deviations).
Other options provided describe different characteristics that do not relate to the normal distribution. For instance, skewed distributions are not symmetrical and can be right (positive) or left (negative) skewed, depending on the direction of the tail. The terms platykurtic and leptokurtic refer to the 'peakedness' of the distribution, where platykurtic has a flatter peak and leptokurtic has a more pronounced peak than a normal distribution. Thus, the correct option that describes the normal distribution is (a) Symmetric and bell-shaped.