A standard distribution has which characteristics?

A standard distribution has which characteristics?

• A. A predetermined mean and standard deviation.
• B. A fixed median and mode.
• C. A random mean and variance.
• D. A zero mean with unit variance.

Answer: (A)

The standard normal distribution is defined by fixed parameters: a mean of zero and a standard deviation of one. This specific pairing (zero mean, unit variance) makes it a universal reference for standardizing any normal variable, using the z-score transformation z = (X − μ)/σ. Because of these fixed values, you can compare different normal variables on the same scale. Other descriptions describe distributions with arbitrary or random parameters, or properties like symmetry, but they don’t capture what makes the standard form uniquely defined. So the correct description is zero mean with unit variance.

The standard normal distribution is defined by fixed parameters: a mean of zero and a standard deviation of one. This specific pairing (zero mean, unit variance) makes it a universal reference for standardizing any normal variable, using the z-score transformation z = (X − μ)/σ. Because of these fixed values, you can compare different normal variables on the same scale. Other descriptions describe distributions with arbitrary or random parameters, or properties like symmetry, but they don’t capture what makes the standard form uniquely defined. So the correct description is zero mean with unit variance.