This transforms the data set into one which has a mean of 0 and a standard deviation of 1, and enables inferences and comparisons of distributions to be achieved simply. 2 giving the distribution shown in Fig. 8 having a mean of 0 and a standard deviation of 1. The area under the curve in Fig. 8 sums to 1.0 and the area between two Z values represents the occurrence of points in a normally distributed data set that have those Z values.
Special tables exist to detail the area under the curve for any Z values.
Table 1 detail areas between 0 and the Z value and above, or below a given Z value. If an area beyond a positive Z value is required, this is termed a one sided tail, while if the areas beyond a positive and negative Z value are required, this is a two sided tail. These tables are used to infer information about the occurrence of certain data points in a distribution Table 1. 0.1587 0.5 Confidence Intervals As indicated earlier, the normal distribution curve has properties which allow probabilities of occurrence to be linked to areas under the curve. By establishing an interval on the Z scale, it is possible to determine the area under the curve between the two Z values, and this area is the probability or confidence of occurrence.