The Standard Normal Curve

The binomial probability distribution is applicable for trials with two potential outcomes; in other words, it is used for dichotomous categorical variables. Criminal justice and criminology researchers, however, often use continuous variables. The binomial probability distribution has no applicability in this context. Continuous variables are represented by a theoretical distribution called the normal curve.

Normal curve: A distribution of raw scores from a sample or population that is symmetric and unimodal and has an area of 1.00. Normal curves are expressed in raw units and differ from one another in metrics, means, and standard deviations.

The normal curve is a unimodal , symmetric curve with an area of 1.00. It is unimodal because it peaks once and only once. In other words, it has one modal value. It is symmetric because the two halves (split by the mean) are identical to one another. Additionally, it has an area of 1.00 because it encompasses all possible values of the variable in question. Just as the binomial probability distribution’s p (r) column always sums to 1.00 because all values that r could possibly take on are contained within the table, so too the normal curve’s tails stretch out to negative and positive infinity. This might sound impossible, but remember that this is a theoretical distribution. This curve is built on probabilities, not on actual data.