What are the two parameters that define a normal distribution?

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Accepted Answer

Mean (μ) and standard deviation (σ). A normal distribution is completely defined by two parameters: the mean (μ), which determines the center of the distribution, and the standard deviation (σ), which determines the spread or width. Different combinations of μ and σ produce different normal curves, but all share the characteristic bell shape and symmetry about the mean.

Sample size (n) and probability (p) are the parameters of the binomial distribution, not the normal distribution; these determine the number of trials and the probability of success in each trial. Minimum and maximum values would define a uniform distribution, not a normal distribution; the normal distribution theoretically extends from negative infinity to positive infinity. The median and mode of a normal distribution are equal to the mean, so specifying them would be redundant; the spread (standard deviation) is also needed.

Understanding the normal distribution is essential for the DSST exam. Students should know that changing μ shifts the curve left or right without changing its shape, while changing σ makes the curve wider (larger σ) or narrower (smaller σ). The standard normal distribution has μ = 0 and σ = 1.

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