The normal distribution is a model distribution which many sets of data fall upon. It can be proven that the sums of

draws from a box approaches normal distribution as the number of draws approaches

infinity, no matter what is in the box (as long as there are at least two distinct values). The

bell curve, or normal distribution curve, is a very useful model of perfect normal distribution. The formula for the bell curve is

e^{-x2/2} / sqrt(2

pi). The

area under this distribution curve is one, and the

mean,

median, and

mode all occur at 0, and the curve is

symmetric around the

y-axis. This curve has no integral--therefore it is necessary to use

numerical integration or a table to find integrals.

Here is a table of integrals of the normal distribution from 0 to z:

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
-------------------------------------------------------------------------
.0| .0000 .0040 .0080 .0120 .0159 .0199 .0239 .0279 .0319 .0359
.1| .0398 .0438 .0477 .0517 .0557 .0596 .0635 .0675 .0714 .0753
.2| .0792 .0832 .0871 .0909 .0948 .0987 .1026 .1064 .1102 .1141
.3| .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517
.4| .1554 .1591 .1627 .1664 .1700 .1736 .1772 .1808 .1844 .1879
.5| .1915 .1950 .1985 .2019 .2054 .2088 .2122 .2156 .2190 .2224
.6| .2257 .2291 .2324 .2356 .2389 .2421 .2454 .2486 .2517 .2549
.7| .2580 .2611 .2642 .2673 .2703 .2734 .2764 .2793 .2823 .2852
.8| .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133
.9| .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3364 .3389
1.0| .3413 .3437 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621
1.1| .3643 .3665 .3686 .3707 .3728 .3749 .3770 .3790 .3810 .3830
1.2| .3849 .3868 .3888 .3906 .3925 .3943 .3962 .3979 .3997 .4015
1.3| .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4146 .4162 .4177
1.4| .4192 .4207 .4222 .4236 .4251 .4265 .4278 .4292 .4306 .4319
1.5| .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441
1.6| .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545
1.7| .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633
1.8| .4641 .4648 .4656 .4664 .4671 .4678 .4685 .4692 .4699 .4706
1.9| .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767
2.0| .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817
2.1| .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857
2.2| .4861 .4864 .4868 .4871 .4874 .4878 .4881 .4884 .4887 .4890
2.3| .4893 .4895 .4898 .4901 .4903 .4906 .4909 .4911 .4913 .4916
2.4| .4918 .4920 .4922 .4924 .4926 .4928 .4930 .4932 .4934 .4936
2.5| .4938 .4940 .4941 .4943 .4944 .4946 .4948 .4949 .4950 .4952
2.6| .4953 .4955 .4956 .4957 .4958 .4960 .4961 .4962 .4963 .4964
2.7| .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974
2.8| .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981
2.9| .4981 .4982 .4982 .4983 .4983 .4984 .4984 .4985 .4985 .4986
3.0| .4986 .4987 .4987 .4988 .4988 .4988 .4989 .4989 .4990 .4990
3.1| .4990 .4991 .4991 .4991 .4991 .4992 .4992 .4992 .4993 .4993
3.2| .4993 .4993 .4993 .4994 .4994 .4994 .4994 .4995 .4995 .4995
3.3| .4995 .4995 .4995 .4996 .4996 .4996 .4996 .4996 .4996 .4996
3.4| .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997
3.5| .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998
3.6| .4998 .4998 .4998 .4998 .4999 .4999 .4999 .4999 .4999 .4999
3.7| .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999
3.8| .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999
3.9|~.5000