3.3 Using the Tables of the Standard Normal Distribution
As already mentioned, the standard normal distribution is extensively tabled. Such a table
can be found in Appendixz, part of which is reproduced in Table 3.1.^1 To see how we can
make use of this table, consider the normal distribution represented in Figure 3.7. This
might represent the standardized distribution of the Behavior Problem scores as seen in
Figure 3.6. Suppose we want to know how much of the area under the curve is above oneSection 3.3 Using the Tables of the Standard Normal Distribution 73(^1) If you prefer electronic tables, many small Java programs are available on the Internet. One of my favorite pro-
grams for calculating zprobabilities is at http://psych.colorado.edu/~mcclella/java/zcalc.html. An online video
displaying properties of the normal distribution is available at http://huizen.dds.nl/~berrie/normal.html.
Table 3.1 The normal distribution (abbreviated version of Appendix z)
0 z
Larger
portion
Smaller
portion
Mean Larger Smaller Mean Larger Smaller
z to z Portion Portion z to z Portion Portion
0.00 0.0000 0.5000 0.5000 0.45 0.1736 0.6736 0.3264
0.01 0.0040 0.5040 0.4960 0.46 0.1772 0.6772 0.3228
0.02 0.0080 0.5080 0.4920 0.47 0.1808 0.6808 0.3192
0.03 0.0120 0.5120 0.4880 0.48 0.1844 0.6844 0.3156
0.04 0.0160 0.5160 0.4840 0.49 0.1879 0.6879 0.3121
0.05 0.0199 0.5199 0.4801 0.50 0.1915 0.6915 0.3085
........................
0.97 0.3340 0.8340 0.1660 1.42 0.4222 0.9222 0.0778
0.98 0.3365 0.8365 0.1635 1.43 0.4236 0.9236 0.0764
0.99 0.3389 0.8389 0.1611 1.44 0.4251 0.9251 0.0749
1.00 0.3413 0.8413 0.1587 1.45 0.4265 0.9265 0.0735
1.01 0.3438 0.8438 0.1562 1.46 0.4279 0.9279 0.0721
1.02 0.3461 0.8461 0.1539 1.47 0.4292 0.9292 0.0708
1.03 0.3485 0.8485 0.1515 1.48 0.4306 0.9306 0.0694
1.04 0.3508 0.8508 0.1492 1.49 0.4319 0.9319 0.0681
1.05 0.3531 0.8531 0.1469 1.50 0.4332 0.9332 0.0668
........................
1.95 0.4744 0.9744 0.0256 2.40 0.4918 0.9918 0.0082
1.96 0.4750 0.9750 0.0250 2.41 0.4920 0.9920 0.0080
1.97 0.4756 0.9756 0.0244 2.42 0.4922 0.9922 0.0078
1.98 0.4761 0.9761 0.0239 2.43 0.4925 0.9925 0.0075
1.99 0.4767 0.9767 0.0233 2.44 0.4927 0.9927 0.0073
2.00 0.4772 0.9772 0.0228 2.45 0.4929 0.9929 0.0071
2.01 0.4778 0.9778 0.0222 2.46 0.4931 0.9931 0.0069
2.02 0.4783 0.9783 0.0217 2.47 0.4932 0.9932 0.0068
2.03 0.4788 0.9788 0.0212 2.48 0.4934 0.9934 0.0066
2.04 0.4793 0.9793 0.0207 2.49 0.4936 0.9936 0.0064
2.05 0.4798 0.9798 0.0202 2.50 0.4938 0.9938 0.0062