Which of the following statements about the shape of a normally distributed data set is true?

• A. The distribution has two peaks.
• B. The distribution is uniform across all values.
• C. The distribution is symmetric about its mean $\mu$.
• D. The distribution is skewed to the right.

Answer: (C)

Verified step by step guidance

1. Recall the definition of a normal distribution: it is a continuous probability distribution characterized by a symmetric, bell-shaped curve centered around its mean.
2. Understand that the shape of a normal distribution is unimodal, meaning it has a single peak, not two peaks, so the statement about two peaks is false.
3. Recognize that a uniform distribution has equal probability across all values, which is different from the bell-shaped curve of a normal distribution, so the uniform statement is false.
4. Note that a normal distribution is symmetric about its mean, meaning the left and right sides of the distribution are mirror images, which supports the correct statement.
5. Remember that skewness refers to asymmetry; since a normal distribution is symmetric, it is not skewed to the right or left, so the skewed statement is false.