In a standard normal distribution, what are the mean and standard deviation?

In a standard normal distribution, what are the mean and standard deviation?

• A. Mean 0 and standard deviation 1.
• B. Mean 0 and standard deviation 2.
• C. Mean 1 and standard deviation 1.
• D. Mean -1 and standard deviation 1.

Answer: (A)

The standard normal distribution is a normal distribution with mean zero and standard deviation one. This form comes from standardizing any normal variable X by Z = (X − μ)/σ, which centers the distribution at 0 and fixes the spread at 1. That standardization lets us use the z-table to find probabilities. So the defining description is a mean of 0 and a standard deviation of 1. The other options describe different normal distributions because they either shift the center away from zero or change the spread away from one.

The standard normal distribution is a normal distribution with mean zero and standard deviation one. This form comes from standardizing any normal variable X by Z = (X − μ)/σ, which centers the distribution at 0 and fixes the spread at 1. That standardization lets us use the z-table to find probabilities. So the defining description is a mean of 0 and a standard deviation of 1. The other options describe different normal distributions because they either shift the center away from zero or change the spread away from one.