The distribution Z ∼ N(0, 1) is known as the

The distribution Z ∼ N(0, 1) is known as the

• A. Normal distribution
• B. Uniform distribution
• C. Standard normal distribution
• D. Exponential distribution

Answer: (C)

A normal distribution with mean zero and unit variance is called the standard normal distribution. Since Z follows N(0,1), it sits at the center of the normal family with no shift and the smallest possible spread that still scales to a bell shape. This standard form is what you get when you convert any normal variable X with mean μ and standard deviation σ into a Z-score: Z = (X − μ)/σ, which then follows the standard normal distribution. The other options describe different families: a normal distribution in general can have any mean and variance; a uniform distribution has constant density on an interval; and an exponential distribution is skewed with a single rate parameter.

A normal distribution with mean zero and unit variance is called the standard normal distribution. Since Z follows N(0,1), it sits at the center of the normal family with no shift and the smallest possible spread that still scales to a bell shape. This standard form is what you get when you convert any normal variable X with mean μ and standard deviation σ into a Z-score: Z = (X − μ)/σ, which then follows the standard normal distribution. The other options describe different families: a normal distribution in general can have any mean and variance; a uniform distribution has constant density on an interval; and an exponential distribution is skewed with a single rate parameter.