“Critical" values of z are associated with interesting central areas under the standard normal curve. For instance, as seen in the picture to the right, there is an 80% probability that any normal variable will have a zscore between –1.28 and 1.28. In other words, there is an 80% probability that any normal variable will fall within 1.28 standard deviations of its mean. So we say that 1.28 is the critical value of z that corresponds to a central area of 0.80. To any central area there corresponds a “tail area." (This is yellow in the picture.) Since there are two “tails", the central area is always 1  2(tail area), and the tail area is always 0.5(1 – central area). Critical z values are often denoted by z_{α}, where the subscript α (alpha) is the tail area. For instance, the picture on the right indicates that The four pictures below illustrate other important critical values of z. 





These five critical values of z are summarized in the following table.

















