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

• A. $0$
• B. $\mu$
• C. $\mu +\sigma$
• D. $\sigma$

Answer: (B)

Verified step by step guidance

1. Recall the definition of a normal distribution, which is characterized by two parameters: the mean (\mu) and the standard deviation (\sigma).
2. Understand that the mean (\mu) of a normal distribution represents the central location or the expected value of the distribution.
3. Recognize that the standard deviation (\sigma) measures the spread or dispersion of the distribution around the mean, but does not affect the mean itself.
4. Therefore, the mean of the normal distribution is simply the parameter \mu, regardless of the value of \sigma.
5. Conclude that the mean of the distribution is \mu, not 0, \mu + \sigma, or \sigma.