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. μ = 0, σ = 1
• B. μ = 1, σ = 0
• C. μ = -1, σ = 2
• D. μ = 0, σ = 2

Answer: (A)

A standard normal distribution is a normal distribution that has been standardized so the center is at zero and the spread is measured in units of the standard deviation. The mean is 0 because the curve is symmetric around zero, and the standard deviation is 1 because we rescale so one unit reflects one standard deviation. This standardization lets us convert any normal variable X ~ N(μ, σ^2) into Z = (X − μ)/σ, giving Z ~ N(0, 1). So the standard normal has μ = 0 and σ = 1. Any other combination would describe a different normal distribution, not the standard one.

A standard normal distribution is a normal distribution that has been standardized so the center is at zero and the spread is measured in units of the standard deviation. The mean is 0 because the curve is symmetric around zero, and the standard deviation is 1 because we rescale so one unit reflects one standard deviation. This standardization lets us convert any normal variable X ~ N(μ, σ^2) into Z = (X − μ)/σ, giving Z ~ N(0, 1). So the standard normal has μ = 0 and σ = 1. Any other combination would describe a different normal distribution, not the standard one.