Which statement about the standard normal distribution is true?

Which statement about the standard normal distribution is true?

• A. It has mean 1 and standard deviation 0
• B. It has mean 0 and standard deviation 1
• C. It is skewed to the right
• D. It is uniform

Answer: (B)

The standard normal distribution is the normal distribution scaled so that its mean is zero and its standard deviation is one. You get it by converting any normal variable X with mean μ and standard deviation σ into Z = (X − μ)/σ. This standardization centers the distribution at zero and assigns a unit spread, so the defining properties are a mean of 0 and a standard deviation of 1. It’s the bell-shaped, symmetric curve used to compute probabilities with z-scores. That’s why the statement stating mean zero and standard deviation one is true. The other ideas don’t fit: a distribution with mean 1 and standard deviation 0 would collapse to a single point and isn’t a normal distribution; the standard normal is symmetric about zero, not skewed; and it is not uniform, as it has the characteristic bell-shaped density.

The standard normal distribution is the normal distribution scaled so that its mean is zero and its standard deviation is one. You get it by converting any normal variable X with mean μ and standard deviation σ into Z = (X − μ)/σ. This standardization centers the distribution at zero and assigns a unit spread, so the defining properties are a mean of 0 and a standard deviation of 1. It’s the bell-shaped, symmetric curve used to compute probabilities with z-scores.

That’s why the statement stating mean zero and standard deviation one is true. The other ideas don’t fit: a distribution with mean 1 and standard deviation 0 would collapse to a single point and isn’t a normal distribution; the standard normal is symmetric about zero, not skewed; and it is not uniform, as it has the characteristic bell-shaped density.