For a standard normal distribution, what is the mean $\mu$ and standard deviation $\sigma$?

• A. Mean $1$, standard deviation $0$
• B. Mean $1$, standard deviation $2$
• C. Mean $0$, standard deviation $0.5$
• D. Mean $0$, standard deviation $1$

Answer: (D)

Verified step by step guidance

1. Recall the definition of a standard normal distribution: it is a normal distribution that has been standardized to have a mean of 0 and a standard deviation of 1.
2. Understand that the mean (\( \mu \)) represents the center or average value of the distribution.
3. Recognize that the standard deviation (\( \sigma \)) measures the spread or dispersion of the distribution around the mean.
4. For a standard normal distribution, by definition, the mean is \( \mu = 0 \) and the standard deviation is \( \sigma = 1 \).
5. Therefore, among the given options, the correct parameters for the standard normal distribution are mean 0 and standard deviation 1.