Which of the following is true regarding the standard normal distribution?

• A. It is always skewed to the right.
• B. It has a mean of $0$ and a standard deviation of $1$.
• C. It has a mean of $1$ and a standard deviation of $0$.
• D. Its total area under the curve is less than $1$.

Answer: (B)

Verified step by step guidance

1. Recall the definition of the standard normal distribution: it is a special case of the normal distribution with a mean (\mu) of 0 and a standard deviation (\sigma) of 1.
2. Understand that the standard normal distribution is symmetric about its mean, so it is not skewed to the right or left; it has zero skewness.
3. Remember that the total area under any probability density function (PDF) curve, including the standard normal distribution, must equal 1, representing the total probability.
4. Evaluate each statement based on these properties: check the mean and standard deviation values, the skewness, and the total area under the curve.
5. Conclude that the true statement is the one that correctly states the mean is 0 and the standard deviation is 1, consistent with the standard normal distribution's definition.