A normal distribution is a bell-shaped distribution. Theoretically, a normal distribution is continuous and may be depicted as a density curve, such as the one below.The distribution plot belowis astandard normal distribution.A standard normal distribution has a mean of 0 and standard deviation of 1. This is also known as thez distribution. You may see the notation \(N(\mu, \sigma\)) where N signifies that the distribution is normal, \(\mu\) is the mean of the distribution, and \(\sigma\) is the standard deviation of the distribution. A z distribution may be described as \(N(0,1)\).
While we cannot determine the probability for any one given value because the distribution is continuous, we can determine the probability for a given interval of values.The probability for an interval is equal to the area under the density curve. The total area under the curve is 1.00, or 100%.In other words, 100% of observations fall under the curve.
For example, inLesson 2we learned about the Empirical Rule which stated that approximately 68% of observations on a normal distribution will fall within one standard deviation of the mean, approximately 95% will fall within two standard deviations of the mean, and approximately 99.7% will fall within three standard deviations of the mean.
