z score table for standard normal distribution

Here, X is a normal random variable, µ is the mean of X and σ is the standard deviation of X. A normal random variable can be transformed into a z-score using the following equation.

The normal random variable of a standard normal distribution is called as a standard score or z-score. Standardization is the process of transforming a normal distribution into a standard normal distribution, it is also called z-transformation. Therefore, the pdf of a standard normal distribution will be given by Mathematically, the probability density function (pdf) of a standard normal distribution is obtained by substituting the values µ = 0 & σ = 1 in the pdf of the normal distribution, discussed in the previous section of the article. This distribution is also known as Z-distribution. The Standard Normal distribution is a special case of normal distribution where mean is zero (µ = 0) and standard deviation is one (σ = 1) and it is abbreviated as N(0, 1). Standard Normal Distribution & Standard Score (Z-Score) I recommend you to go through Simplest Explanation of Normal Distribution, for understanding the normal distribution in more detail. Normal distributions fits many natural phenomenon such as, heights and weights of humans, average daily temperature during summers, scores of standardized tests like SAT & GRE and performance rating of employees in an organization etc.Ī good understanding of the concepts and properties of normal distribution is essential for understanding both the standard normal distribution (z-distribution) and standard score (z-score). A small standard deviation produces a steep graph, whereas a large standard deviation produces a flat graph. The figure shown below represents a family of normal distributions differed by their means (µ1 = µ3 = ♔ > µ2) and standard deviations (σ 1 < σ 2 <σ 3 < σ 4). The mean, median and mode are equal due to the symmetry of the distribution. Here, x is a normal random variable, µ is the mean and σ is the standard deviation of the distribution. The mathematical equation of a normal distribution, also called its probability density function (pdf) is given by The area under the normal distribution curve represents probability and is equal to one. The mean determines the location of the center of the graph, and standard deviation determines the height and width of the graph. The shape of the normal distribution curve is determined by two parameters: the mean ( µ) and the standard deviation ( σ), and it is abbreviated as N( µ, σ). The graph of a normal distribution takes the shape of a bell, hence it is also known as bell curve. Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric about its mean.

Z score table for standard normal distribution