What does the total area below a density curve represent?

The total area under a density curve is a fundamental concept in statistics, particularly in the context of probability distributions. This area represents the likelihood of all possible outcomes for a continuous variable. In probability theory, the total area under the curve of a probability density function (PDF) is always equal to one. This is because it encompasses all probabilities associated with the outcomes in the sample space.

When we refer to the "likelihood of all outcomes," we are acknowledging that the area captures the comprehensive probability for any event within that distribution, affirming that the sum of probabilities for all possible outcomes equals one. Thus, the correct choice fits perfectly with the concept of probability density functions, highlighting the relationship between areas under the curve and total probabilities.

This understanding is crucial as it lays the foundation for interpreting various statistical models and calculations involving probabilities.