z score table for standard normal distribution

But first, we need to learn how to calculate the standardized scores that make up a standard normal distribution. These properties enable us to use the normal distribution to understand how scores relate to one another within and across a distribution.

Approximately 99.7% of the area of a normal distribution is within three standard deviations of the mean.

Approximately 95% of the area of a normal distribution is within two standard deviations of the mean.

Approximately 68% of the area of a normal distribution is within one standard deviation of the mean.

Normal distributions represent populations and are defined by two parameters, the mean (μ) and the standard deviation (σ).

Normal distributions are denser in the center and less dense in the tails.The area under the normal curve is equal to 1.0.The mean, median, and mode of a normal distribution are equal.Normal distributions are symmetric around their mean.

Normal distributions differing in mean and standard deviation.Įight features of normal distributions are listed below. We will focus on the Standard Normal Distribution (also known as the Unit Normal Distribution), which has a mean of 0 and a standard deviation of 1 (i.e., the red distribution in Figure 1).įigure 1. What is consistent about all normal distributions is the shape and the proportion of scores within a given distance along the x-axis. These as well as all other normal distributions are symmetric with relatively more values at the center of the distribution and relatively few in the tails. The green (left-most) distribution has a mean of -3 and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the distribution in black (right-most) has a mean of 2 and a standard deviation of 3. Figure 1 shows three normal distributions. Normal distributions can differ in their means and in their standard deviations. Strictly speaking, it is not correct to talk about the normal distribution since there are many normal distributions. It is also called the “Gaussian curve” after the mathematician Karl Friedrich Gauss. The normal distribution is the most important and most widely used distribution in statistics. Moving forward, we now turn our attention to how scores within a distribution are related to one another, how to precisely describe a score’s location within the distribution, and how to compare scores from different distributions. These simple tools, and the principles behind them, will help you interpret information presented to you and understand the basics of a variable. We now understand how to describe and present our data visually and numerically. Discuss the characteristics of a normal distribution.Identify the z-score location on a normal distribution.Describe the effects of standardizing a distribution.Compute and transform z-scores and x-values.

Z score table for standard normal distribution