Explanation : Properties of a Normal Distribution A normal Distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve, which has all of the following properties: 1. The mean, median and mode are equal. 2. The normal curve is bell-shaped and is symmetric about the mean. 3. The total area under the curve is equal to one. 4. The normal curve approaches, but never touches the x-axis. 5. Between μ – σ and μ + σ the graph is concave down and elsewhere the graph is concave up. The points at which the graph changes concavity are called inflection points. Remarks ∎ A normal distribution can have any mean and any positive standard deviation ∎ The two parameters, μ and s completely determine the shape of the normal curve. ∎ The equation of the normal curve is