How to use this table: Because the normal curve is symmetrical about a mean of zero (the left side being a mirror image of the right side), the areas corresponding to negative z-scores are identical to the areas of positive z-scores. For example, the areas corresponding to a z-score of - 1.00 are the same as those areas of a z-score of + 1.00. Z-scores are given in column A. Areas between (inside) the mean and the z-score are given in column B, and column C contains the area that lies beyond (outside) the z-score. And, since the curve is symmetric, each half of the curve contains .5000 of the total area.
(A) Z | (B) area inside & Z | (C) area outside Z |
---|---|---|
0.00 | .0000 | .5000 |
0.01 | .0040 | .4960 |
0.02 | .0080 | .4920 |
0.03 | .0120 | .4880 |
0.04 | .0160 | .4840 |
0.05 | .0199 | .4801 |
0.06 | .0239 | .4761 |
0.07 | .0279 | .4721 |
0.08 | .0319 | .4681 |
0.09 | .0359 | .4641 |
0.10 | .0398 | .4602 |
0.11 | .0438 | .4562 |
0.12 | .0478 | .4522 |
0.13 | .0517 | .4483 |
0.14 | .0557 | .4443 |
0.15 | .0596 | .4404 |
0.16 | .0636 | .4364 |
0.17 | .0675 | .4325 |
0.18 | .0714 | .4286 |
0.19 | .0753 | .4247 |
0.20 | .0793 | .4207 |
0.21 | .0823 | .4168 |
0.22 | .0871 | .4129 |
0.23 | .0910 | .4090 |
0.24 | .0948 | .4052 |
0.25 | .0987 | .4013 |
0.26 | .1026 | .3974 |
0.27 | .1064 | .3936 |
0.28 | .1103 | .3897 |
0.29 | .1141 | .3859 |
0.30 | .1179 | .3821 |
0.31 | .1217 | .3783 |
0.32 | .1255 | .3745 |
0.33 | .1293 | .3707 |
0.34 | .1331 | .3669 |
0.35 | .1368 | .3632 |
0.36 | .1406 | .3594 |
0.37 | .1443 | .3557 |
0.38 | .1480 | .3520 |
0.39 | .1517 | .3483 |
0.40 | .1551 | .3446 |
0.41 | .1591 | .3409 |
0.42 | .1628 | .3372 |
0.43 | .1664 | .3336 |
0.44 | .1700 | .3300 |
0.45 | .1736 | .3264 |
0.46 | .1772 | .3228 |
0.47 | .1808 | .3190 |
0.48 | .1844 | .3156 |
0.49 | .1879 | .3121 |
0.50 | .1915 | .3085 |
0.51 | .1950 | .3050 |
0.52 | .1985 | .3015 |
0.53 | .2019 | .2981 |
0.54 | .2054 | .2946 |
0.55 | .2088 | .2912 |
0.56 | .2123 | .2877 |
0.57 | .2157 | .2843 |
0.58 | .2190 | .2810 |
0.59 | .2224 | .2776 |
0.60 | .2257 | .2743 |
0.61 | .2291 | .2709 |
0.62 | .2324 | .2676 |
0.63 | .2357 | .2643 |
0.64 | .2389 | .2611 |
0.65 | .2422 | .2578 |
0.66 | .2454 | .2546 |
0.67 | .2486 | .2514 |
0.68 | .2517 | .2483 |
0.69 | .2549 | .2451 |
0.70 | .2580 | .2420 |
0.71 | .2611 | .2389 |
0.72 | .2642 | .2358 |
0.73 | .2673 | .2327 |
0.74 | .2704 | .2296 |
0.75 | .2734 | .2266 |
0.76 | .2764 | .2236 |
0.77 | .2794 | .2206 |
0.78 | .2823 | .2177 |
0.79 | .2852 | .2148 |
0.80 | .2881 | .2119 |
0.81 | .2910 | .2090 |
0.82 | .2939 | .2061 |
0.83 | .2967 | .2033 |
0.84 | .2995 | .2005 |
0.85 | .3023 | .1977 |
0.86 | .3051 | .1949 |
0.87 | .3078 | .1922 |
0.88 | .3106 | .1894 |
0.89 | .3133 | .1867 |
0.90 | .3159 | .1841 |
0.91 | .3186 | .1814 |
0.92 | .3212 | .1788 |
0.93 | .3238 | .1762 |
0.94 | .3264 | .1736 |
0.95 | .3289 | .1711 |
0.96 | .3315 | .1685 |
0.97 | .3340 | .1660 |
0.98 | .3365 | .1635 |
0.99 | .3389 | .1611 |
1.00 | .3413 | .1587 |
1.01 | .3438 | .1562 |
1.02 | .3461 | .1539 |
1.03 | .3485 | .1515 |
1.04 | .3508 | .1492 |
1.05 | .3531 | .1469 |
1.06 | .3554 | .1446 |
1.07 | .3577 | .1423 |
1.08 | .3599 | .1410 |
1.09 | .3621 | .1379 |
1.10 | .3643 | .1357 |
1.11 | .3665 | .1335 |
1.12 | .3686 | .1314 |
1.13 | .3708 | .1292 |
1.14 | .3729 | .1271 |
1.15 | .3749 | .1251 |
1.16 | .3770 | .1230 |
1.17 | .3790 | .1210 |
1.18 | .3810 | .1190 |
1.19 | .3830 | .1170 |
1.20 | .3849 | .1151 |
1.21 | .3869 | .1131 |
1.22 | .3888 | .1112 |
1.23 | .3907 | .1093 |
1.24 | .3925 | .1075 |
1.25 | .3944 | .1056 |
1.26 | .3962 | .1038 |
1.27 | .3980 | .1020 |
1.28 | .3997 | .1003 |
1.29 | .4015 | .0985 |
1.30 | .4032 | .0968 |
1.31 | .4049 | .0951 |
1.32 | .4066 | .0934 |
1.33 | .4082 | .0918 |
1.34 | .4099 | .0901 |
1.35 | .4115 | .0885 |
1.36 | .4131 | .0869 |
1.37 | .4147 | .0853 |
1.38 | .4162 | .0838 |
1.39 | .4177 | .0823 |
1.40 | .4192 | .0808 |
1.41 | .4207 | .0793 |
1.42 | .4222 | .0778 |
1.43 | .4236 | .0764 |
1.44 | .4251 | .0749 |
1.45 | .4265 | .0735 |
1.46 | .4279 | .0721 |
1.47 | .4292 | .0708 |
1.48 | .4306 | .0694 |
1.49 | .4319 | .0681 |
1.50 | .4332 | .0668 |
1.51 | .4345 | .0655 |
1.52 | .4357 | .0643 |
1.53 | .4370 | .0630 |
1.54 | .4382 | .0618 |
1.55 | .4394 | .0606 |
1.56 | .4406 | .0594 |
1.57 | .4418 | .0582 |
1.58 | .4429 | .0571 |
1.59 | .4441 | .0559 |
1.60 | .4452 | .0548 |
1.61 | .4463 | .0537 |
1.62 | .4474 | .0526 |
1.63 | .4484 | .0516 |
1.64 | .4495 | .0505 |
1.65 | .4505 | .0495 |
1.66 | .4515 | .0485 |
1.67 | .4525 | .0475 |
1.68 | .4535 | .0465 |
1.69 | .4545 | .0455 |
1.70 | .4554 | .0446 |
1.71 | .4564 | .0436 |
1.72 | .4573 | .0427 |
1.73 | .4582 | .0418 |
1.74 | .4591 | .0409 |
1.75 | .4599 | .0401 |
1.76 | .4608 | .0392 |
1.77 | .4616 | .0384 |
1.78 | .4625 | .0375 |
1.79 | .4633 | .0367 |
1.80 | .4641 | .0359 |
1.81 | .4649 | .0351 |
1.82 | .4656 | .0344 |
1.83 | .4664 | .0336 |
1.84 | .4671 | .0329 |
1.85 | .4678 | .0322 |
1.86 | .4686 | .0314 |
1.87 | .4693 | .0307 |
1.88 | .4699 | .0301 |
1.89 | .4706 | .0294 |
1.90 | .4713 | .0287 |
1.91 | .4719 | .0281 |
1.92 | .4276 | .0274 |
1.93 | .4732 | .0268 |
1.94 | .4738 | .0262 |
1.95 | .4744 | .0256 |
1.96 | .4750 | .0250 |
1.97 | .4756 | .0244 |
1.98 | .4761 | .0239 |
1.99 | .4767 | .0233 |
2.00 | .4772 | .0228 |
2.01 | .4778 | .0222 |
2.02 | .4783 | .0217 |
2.03 | .4788 | .0212 |
2.04 | .4793 | .0207 |
2.05 | .4798 | .0202 |
2.06 | .4803 | .0197 |
2.07 | .4808 | .0192 |
2.08 | .4812 | .0188 |
2.09 | .4817 | .0183 |
2.10 | .4821 | .0179 |
2.11 | .4826 | .0174 |
2.12 | .4830 | .0170 |
2.13 | .4834 | .0166 |
2.14 | .4838 | .0162 |
2.15 | .4842 | .0158 |
2.16 | .4846 | .0154 |
2.17 | .4850 | .0150 |
2.18 | .4854 | .0146 |
2.19 | .4857 | .0143 |
2.20 | .4861 | .0139 |
2.21 | .4864 | .0136 |
2.22 | .4868 | .0132 |
2.23 | .4871 | .0129 |
2.24 | .4875 | .0125 |
2.25 | .4878 | .0122 |
2.26 | .4881 | .0119 |
2.27 | .4884 | .0116 |
2.28 | .4887 | .0113 |
2.29 | .4890 | .0110 |
2.30 | .4893 | .0107 |
2.31 | .4896 | .0104 |
2.32 | .4898 | .0102 |
2.33 | .4901 | .0099 |
2.34 | .4904 | .0096 |
2.35 | .4906 | .0094 |
2.36 | .4909 | .0091 |
2.37 | .4911 | .0089 |
2.38 | .4913 | .0087 |
2.39 | .4916 | .0084 |
2.40 | .4918 | .0082 |
2.41 | .4920 | .0080 |
2.42 | .4922 | .0078 |
2.43 | .4925 | .0075 |
2.44 | .4927 | .0073 |
2.45 | .4929 | .0071 |
2.46 | .4931 | .0069 |
2.47 | .4932 | .0068 |
2.48 | .4934 | .0066 |
2.49 | .4936 | .0064 |
2.50 | .4938 | .0062 |
2.51 | .4940 | .0060 |
2.52 | .4941 | .0059 |
2.53 | .4943 | .0057 |
2.54 | .4945 | .0055 |
2.55 | .4946 | .0054 |
2.56 | .4948 | .0052 |
2.57 | .4949 | .0051 |
2.58 | .4951 | .0049 |
2.59 | .4952 | .0048 |
2.60 | .4953 | .0047 |
2.61 | .4955 | .0045 |
2.62 | .4956 | .0044 |
2.63 | .4957 | .0043 |
2.64 | .4959 | .0041 |
2.65 | .4960 | .0040 |
2.66 | .4961 | .0039 |
2.67 | .4962 | .0038 |
2.68 | .4963 | .0037 |
2.69 | .4964 | .0036 |
2.70 | .4965 | .0035 |
2.71 | .4966 | .0034 |
2.72 | .4967 | .0033 |
2.73 | .4968 | .0032 |
2.74 | .4969 | .0031 |
2.75 | .4970 | .0030 |
2.76 | .4971 | .0029 |
2.77 | .4972 | .0028 |
2.78 | .4973 | .0027 |
2.79 | .4974 | .0026 |
2.80 | .4974 | .0026 |
2.81 | .4975 | .0025 |
2.82 | .4976 | .0024 |
2.83 | .4977 | .0023 |
2.84 | .4977 | .0023 |
2.85 | .4978 | .0022 |
2.86 | .4979 | .0021 |
2.87 | .4979 | .0021 |
2.88 | .4980 | .0020 |
2.89 | .4981 | .0019 |
2.90 | .4981 | .0019 |
2.91 | .4982 | .0018 |
2.92 | .4982 | .0018 |
2.93 | .4983 | .0017 |
2.94 | .4984 | .0016 |
2.95 | .4984 | .0016 |
2.96 | .4985 | .0015 |
2.97 | .4985 | .0015 |
2.98 | .4986 | .0014 |
2.99 | .4986 | .0014 |
3.00 | .4987 | .0013 |
3.01 | .4987 | .0013 |
3.02 | .4987 | .0013 |
3.03 | .4988 | .0012 |
3.04 | .4988 | .0012 |
3.05 | .4989 | .0011 |
3.06 | .4989 | .0011 |
3.07 | .4989 | .001l |
3.08 | .4990 | .0010 |
3.09 | .4990 | .0010 |
3.10 | .4990 | .0010 |
3.11 | .4991 | .0009 |
3.12 | .4991 | .0009 |
3.13 | .4991 | .0009 |
3.14 | .4992 | .0008 |
3.15 | .4992 | .0008 |
3.16 | .4992 | .0008 |
3.17 | .4992 | .0008 |
3.18 | .4993 | .0007 |
3.19 | .4993 | .0007 |
3.20 | .4993 | .0007 |
3.21 | .4993 | .0007 |
3.22 | .4994 | .0006 |
3.23 | .4994 | .0006 |
3.24 | .4994 | .0006 |
3.25 | .4994 | .0006 |
3.30 | .4995 | .0005 |
3.35 | .4996 | .0004 |
3.40 | .4997 | .0003 |
3.45 | .4997 | .0003 |
3.50 | .4998 | .0002 |
3.55 | .4998 | .0002 |
3.60 | .4998 | .0002 |
3.65 | .4999 | .0001 |
3.70 | .4999 | .0001 |
3.75 | .4999 | .0001 |
3.80 | .4999 | .0001 |
3.85 | .4999 | .0001 |
3.90 | .49995 | .00005 |
4.00 | .49997 | .00003 |
Critical values computed by John Timko. Used by permission. |
Sigma(σ) | Centered | Shifted 1.5 σ | ||
---|---|---|---|---|
4.00 | 63[*] | 99.9937[**] | 6210[*] | 99.379 |
5.00 | 0.57 | 99.999943 | 233 | 99.9767 |
6.00 | 0.002[†] | 99.9999998 | 3.4[‡] | 99.99966 |
[*]Defects per Million Opportunities (DPMO).
[**]% yield.
[†]At 6 σ, with a centered distribution (no variation shift), this figure is 2 defects per billion opportunities.
[‡]At 6 σ, with an off-centered distribution (Motorola's 1.5 σ long-term process variation shift average), is the often quoted statement "No more than 3.4 defects per million opportunities." |