Ask AI: Why is the area under a bell - shaped curve equal to one?

The area under a bell-shaped curve, also known as a normal distribution curve or Gaussian curve, is equal to one due to the properties of probability. The curve represents a probability distribution—this means that the total probability of all possible outcomes must equal to 1. When you integrate (find the area under) the curve of the probability density function for a normal distribution, which is bell-shaped, the result is the total probability of all outcomes, so it equals to one. Essentially, this is saying that the total probability of some event within the defined parameters happening is 100%, hence the area under the curve must equal 1 (or 100% when expressed as a percentage).