A normal distribution is determined by two parameters.

A normal distribution is determined by two parameters.

• A. Variance and skewness
• B. Mean and standard deviation
• C. Median and range
• D. Mean and standard deviation

Answer: (D)

A normal distribution is fully determined by its center and its spread. The center is the mean, which tells you where the curve sits on the number line. The spread is the standard deviation, which tells you how wide or narrow the curve is. Together they uniquely specify the distribution; the standard form uses two parameters, μ (the mean) and σ (the standard deviation), with the density function showing how those two numbers shape the curve. Why the other ideas don’t fit: variance and skewness aren’t the defining pair. Variance is simply σ², so it’s not a separate parameter from standard deviation in the usual description. Skewness describes asymmetry, but a normal distribution is symmetric, so skewness isn’t a defining parameter. Median and range don’t fix the entire shape or scale of the distribution—range depends on the sample and does not determine the distribution parameters.

A normal distribution is fully determined by its center and its spread. The center is the mean, which tells you where the curve sits on the number line. The spread is the standard deviation, which tells you how wide or narrow the curve is. Together they uniquely specify the distribution; the standard form uses two parameters, μ (the mean) and σ (the standard deviation), with the density function showing how those two numbers shape the curve.

Why the other ideas don’t fit: variance and skewness aren’t the defining pair. Variance is simply σ², so it’s not a separate parameter from standard deviation in the usual description. Skewness describes asymmetry, but a normal distribution is symmetric, so skewness isn’t a defining parameter. Median and range don’t fix the entire shape or scale of the distribution—range depends on the sample and does not determine the distribution parameters.