Not a characteristic of the normal probability distribution

D

The normal probability distribution is not skewed but bell shaped and symmetric.

The normal probability distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is widely used in various fields, including finance and statistics. It is characterized by several key features, and your question asks you to identify the characteristic that does not apply to the normal distribution.

Let's analyze each answer choice:

A. Bell shaped: The normal distribution is known for its bell-shaped curve, which means that it is symmetric around its mean. The majority of the data falls around the mean, and as you move away from the mean, the frequency of data points decreases gradually. This characteristic is central to understanding the normal distribution, and it is a defining feature.

B. Symmetrical: As mentioned above, the normal distribution is symmetric. This means that if you were to fold the curve in half at its peak (mean), both halves would perfectly overlap. The left and right tails of the distribution mirror each other. Thus, symmetry is a fundamental property of the normal distribution.

C. All of these answers: This answer choice suggests that all of the given characteristics-bell shaped, symmetrical, and asymptotic-are not applicable to the normal distribution. However, we have already established that the normal distribution is bell-shaped and symmetrical, so this answer choice is incorrect.

D. Positively skewed: Skewness refers to the measure of asymmetry in a distribution. If a distribution is positively skewed, it means that its tail on the right side is longer or more stretched out compared to the left tail. In a normal distribution, the tails are symmetric, and there is no skewness. Therefore, a normal distribution is not positively skewed. This answer choice is correct.

E. Asymptotic: Asymptotic means that the tails of the distribution approach but never touch the horizontal axis. In a normal distribution, the tails do become increasingly close to the horizontal axis but technically never touch it. Hence, the normal distribution is asymptotic. This means that answer choice E is incorrect.

To summarize, the characteristic that does not apply to the normal probability distribution is D. Positively skewed. The normal distribution is bell-shaped, symmetrical, and asymptotic, but it does not exhibit skewness.