It is important to note that this discussion applies mainly to populations rather than samples. As such, the area under the entire normal curve (which extends to positive and negative infinity) is unity. Recall that a probability for a distribution is associated with the area under the curve for a particular range of values. We can also calculate probabilities of the form P( a < X ≤ b)-in such cases, the shaded region would be more limited. This expression, which calculates the area under the curve from the extreme left (negative infinity) to x = c, refers to the shaded region shown below. Although you need not fully understand the following notation, the probability P( X ≤ x) can be written as Furthermore, the distribution can easily be scaled to conform to the particular mean and standard deviation of interest. Nevertheless, because the normal distribution applies to so many different situations, tables containing probabilities for ranges of values are readily available. The general form of the normal distribution is shown below note the "bell-curve" shape of the graph, and note that the distribution is symmetric about the mean (peak).īecause this distribution is continuous, integral calculus is required to directly calculate associated probabilities. In this formula, μ is the mean of the distribution and σ is the standard deviation. This distribution is known as the normal distribution (or, alternatively, the Gauss distribution or bell curve), and it is a continuous distribution having the following algebraic expression for the probability density. (Be aware that this table is slightly different than the type of table used to solve the problems in the article-the difference is discussed, however.)Ī number of different types of specific distributions have various applications, but one distribution in particular is heavily used (and well known) across a wide range of areas. O A table of values for the standard normal distribution is available at. O Calculate probabilities for normally distributed data
#STANDARD NORMAL TABLE PROBABILITY HOW TO#
O Know how to standardize a random variable using the Z-score O Recognize the normal distribution and its fundamental characteristics
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