Final answer:
The characteristic not true of a normal probability distribution is C) Skewed distribution. A normal distribution is symmetric, bell-shaped, where the mean, median, and mode are equal, and the standard deviation is never zero.
Step-by-step explanation:
The characteristic which is not true of a normal probability distribution is C) Skewed distribution. The normal probability distribution has several distinct characteristics that define its shape and the way data is distributed around the mean.
Normal distribution is depicted as a bell-shaped curve that is symmetrical around the mean, which is its center. This symmetry implies that the mean, median, and mode are all equal and fall at the center of the distribution. Thus, the correct answer A) Bell-shaped curve and B) Symmetrical around the mean are valid characteristics of a normal distribution.
Furthermore, the total area under the curve is one, signifying that it represents the entire range of possible outcomes for a given set of data. But when we talk about a skewed distribution, it refers to a scenario where the data points are not evenly distributed around the mean. In a normal distribution, however, the data is not skewed—it's evenly balanced on both sides of the mean. Therefore, a skewed distribution is not characteristic of a normal distribution.
Lastly, regarding option D) Standard deviation equals zero, this would imply that all data points are the same, which is not the case in a normal distribution. Standard deviation in a normal distribution measures the spread of data around the mean, and is never zero (except when all data points are identical).