Which of the following is a characteristic of the standard normal distribution?

• A. It is uniform on the interval $[0,1]$.
• B. It is symmetric about 0 and has mean $0$ and standard deviation $1$.
• C. It is symmetric about 0 and has mean $1$ and standard deviation $0$.
• D. It is skewed to the right and has mean $0$ and standard deviation $1$.

Answer: (B)

Verified step by step guidance

1. Recall the definition of the standard normal distribution: it is a normal distribution with a mean of 0 and a standard deviation of 1.
2. Understand that the standard normal distribution is symmetric about its mean, which means the left and right sides of the distribution are mirror images.
3. Recognize that the standard normal distribution is not uniform; a uniform distribution has equal probability across an interval, which is not the case here.
4. Note that the standard deviation cannot be zero for a normal distribution because that would imply no variability, which contradicts the nature of the distribution.
5. Conclude that the characteristic 'It is symmetric about 0 and has mean 0 and standard deviation 1' correctly describes the standard normal distribution.