A continuous distribution is completely defined by the:

A continuous distribution is completely defined by the:

• A. mean and median
• B. mean and standard deviation
• C. mode and variance
• D. range and variance

Answer: (B)

The important idea is that a normal distribution is fully specified by two parameters: its location and its spread. The mean sets where the peak of the curve lies, and the standard deviation determines how wide or narrow the curve is. The normal density function depends only on these two numbers, so once you know them, the entire distribution is fixed. Other two-number descriptions don’t pin down the shape of a distribution; for example, mean and median can differ for skewed distributions, and range with variance doesn’t uniquely determine the distribution’s form. So, for a normal distribution, the pair of mean and standard deviation uniquely defines the distribution.

The important idea is that a normal distribution is fully specified by two parameters: its location and its spread. The mean sets where the peak of the curve lies, and the standard deviation determines how wide or narrow the curve is. The normal density function depends only on these two numbers, so once you know them, the entire distribution is fixed. Other two-number descriptions don’t pin down the shape of a distribution; for example, mean and median can differ for skewed distributions, and range with variance doesn’t uniquely determine the distribution’s form. So, for a normal distribution, the pair of mean and standard deviation uniquely defines the distribution.