Which of the following statements is true about the standard normal distribution?

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

Answer: (C)

Verified step by step guidance

1. Recall the definition of the standard normal distribution: it is a normal distribution with a mean (\mu) of 0 and a standard deviation (\sigma) of 1.
2. Understand the shape of the standard normal distribution: it is symmetric about the mean, which means it is not skewed to the right or left; therefore, the statement about it being always skewed to the right is false.
3. Remember that the total area under any probability density function (PDF) curve, including the standard normal distribution, must equal 1, so the statement about the total area being less than 1 is incorrect.
4. Since the standard normal distribution is symmetric, the mean and median are equal, which means the statement that the mean and median are always different is false.
5. Conclude that the true statement is the one that correctly describes the standard normal distribution's parameters: it has a mean of 0 and a standard deviation of 1.