Questions: Which of the following is NOT a descriptor of a normal distribution of a random variable? Choose the correct answer below. A. The graph of the distribution is bell-shaped. B. The graph is centered around 0. C. The graph is centered around the mean. D. The graph of the distribution is symmetric.

Solution Steps

To determine which of the given options is NOT a descriptor of a normal distribution, we need to understand the properties of a normal distribution. A normal distribution is typically bell-shaped, symmetric, and centered around its mean. It is not necessarily centered around 0 unless the mean is 0.

A normal distribution is characterized by several key properties:

1. The graph is bell-shaped.
2. The graph is symmetric about the mean.
3. The mean, median, and mode are all equal.

We need to evaluate the given options:

• A: The graph of the distribution is bell-shaped. (True)
• B: The graph is centered around 0. (Not necessarily true; it depends on the mean.)
• C: The graph is centered around the mean. (True)
• D: The graph of the distribution is symmetric. (True)

From the analysis, option B is the only statement that is not universally true for all normal distributions, as they can be centered around any mean \( \mu \), not just 0.

Final Answer