For example, , using symmetry.
A random variable is said to have a normal distribution if it has a probability distribution that is symmetric and bell-shaped.
First, the total area under the curve is 1. The second is area will be used to measure probabilities. A normal distribution is intimately connected to Z-scores. The main idea is to standardize all the data that is given by using Z-scores. These Z-scores can then be used to find the area (and thus the probability) under the normal curve. Before getting into computing probabilities, here is a quick reminder of Z-scores.