Area
under the normal curve for different values of z: |
|
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|
|
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|
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|
z-score value: |
Area between the mean and z: |
Area beyond z: |
z-score value: |
Area between the mean and z: |
Area beyond z: |
z-score value: |
Area between the mean and z: |
Area beyond z: |
z-score value: |
Area between the mean and z: |
Area beyond z: |
|
0 |
0 |
0.5 |
1 |
0.3413 |
0.1587 |
2 |
0.4772 |
0.0228 |
3 |
0.4987 |
0.0013 |
|
0.01 |
0.004 |
0.496 |
1.01 |
0.3438 |
0.1562 |
2.01 |
0.4778 |
0.0222 |
3.01 |
0.4987 |
0.0013 |
|
0.02 |
0.008 |
0.492 |
1.02 |
0.3461 |
0.1539 |
2.02 |
0.4783 |
0.0217 |
3.02 |
0.4987 |
0.0013 |
|
0.03 |
0.012 |
0.488 |
1.03 |
0.3485 |
0.1515 |
2.03 |
0.4788 |
0.0212 |
3.03 |
0.4988 |
0.0012 |
|
0.04 |
0.016 |
0.484 |
1.04 |
0.3508 |
0.1492 |
2.04 |
0.4793 |
0.0207 |
3.04 |
0.4988 |
0.0012 |
|
0.05 |
0.0199 |
0.4801 |
1.05 |
0.3531 |
0.1469 |
2.05 |
0.4798 |
0.0202 |
3.05 |
0.4989 |
0.0011 |
|
0.06 |
0.0239 |
0.4761 |
1.06 |
0.3554 |
0.1446 |
2.06 |
0.4803 |
0.0197 |
3.06 |
0.4989 |
0.0011 |
How to use this table: |
0.07 |
0.0279 |
0.4721 |
1.07 |
0.3577 |
0.1423 |
2.07 |
0.4808 |
0.0192 |
3.07 |
0.4989 |
0.0011 |
The red
column gives the area under the normal curve that corresponds to the red area
in the graph above. |
0.08 |
0.0319 |
0.4681 |
1.08 |
0.3599 |
0.1401 |
2.08 |
0.4812 |
0.0188 |
3.08 |
0.499 |
0.001 |
The
blue column givers the area under the normal curve that corresponds to the
blue area in the graph above. |
0.09 |
0.0359 |
0.4641 |
1.09 |
0.3621 |
0.1379 |
2.09 |
0.4817 |
0.0183 |
3.09 |
0.499 |
0.001 |
Example: what proportion of the area
under the normal curve falls beyond a z-score of 1.29? |
0.1 |
0.0398 |
0.4602 |
1.1 |
0.3643 |
0.1357 |
2.1 |
0.4821 |
0.0179 |
3.1 |
0.499 |
0.001 |
Answer:
0.0985 of the area under the curve falls beyond this value of z. |
0.11 |
0.0438 |
0.4562 |
1.11 |
0.3665 |
0.1335 |
2.11 |
0.4826 |
0.0174 |
3.11 |
0.4991 |
0.0009 |
What proportion of the area under the
normal curve falls between a z-score of 1.29 and the mean? |
0.12 |
0.0478 |
0.4522 |
1.12 |
0.3686 |
0.1314 |
2.12 |
0.483 |
0.017 |
3.12 |
0.4991 |
0.0009 |
Answer: 0.4015 of the area under the
curve falls within this range. |
0.13 |
0.0517 |
0.4483 |
1.13 |
0.3708 |
0.1292 |
2.13 |
0.4834 |
0.0166 |
3.13 |
0.4991 |
0.0009 |
|
0.14 |
0.0557 |
0.4443 |
1.14 |
0.3729 |
0.1271 |
2.14 |
0.4838 |
0.0162 |
3.14 |
0.4992 |
0.0008 |
Note that the table only gives areas
corresponding topositive
z-scores - i.e., ones falling to the right of the mean. |
0.15 |
0.0596 |
0.4404 |
1.15 |
0.3749 |
0.1251 |
2.15 |
0.4842 |
0.0158 |
3.15 |
0.4992 |
0.0008 |
For negative z-scores (i.e. for areas to the left of the mean on the graph
above) simply look up the z-score as if it |
0.16 |
0.0636 |
0.4364 |
1.16 |
0.377 |
0.123 |
2.16 |
0.4846 |
0.0154 |
3.16 |
0.4992 |
0.0008 |
were
positive. (The normal curve is symmetrical, so negative z-scores cut off the
same proportions ofarea under the |
0.17 |
0.0675 |
0.4325 |
1.17 |
0.379 |
0.121 |
2.17 |
0.485 |
0.015 |
3.17 |
0.4992 |
0.0008 |
curve as do positive z-scores). |
0.18 |
0.0714 |
0.4286 |
1.18 |
0.381 |
0.119 |
2.18 |
0.4854 |
0.0146 |
3.18 |
0.4993 |
0.0007 |
|
0.19 |
0.0753 |
0.4247 |
1.19 |
0.383 |
0.117 |
2.19 |
0.4857 |
0.0143 |
3.19 |
0.4993 |
0.0007 |
|
0.2 |
0.0793 |
0.4207 |
1.2 |
0.3849 |
0.1151 |
2.2 |
0.4861 |
0.0139 |
3.2 |
0.4993 |
0.0007 |
|
0.21 |
0.0832 |
0.4168 |
1.21 |
0.3869 |
0.1131 |
2.21 |
0.4864 |
0.0136 |
3.21 |
0.4993 |
0.0007 |
|
0.22 |
0.0871 |
0.4129 |
1.22 |
0.3888 |
0.1112 |
2.22 |
0.4868 |
0.0132 |
3.22 |
0.4994 |
0.0006 |
|
0.23 |
0.091 |
0.409 |
1.23 |
0.3907 |
0.1093 |
2.23 |
0.4871 |
0.0129 |
3.23 |
0.4994 |
0.0006 |
|
0.24 |
0.0948 |
0.4052 |
1.24 |
0.3925 |
0.1075 |
2.24 |
0.4875 |
0.0125 |
3.24 |
0.4994 |
0.0006 |
|
0.25 |
0.0987 |
0.4013 |
1.25 |
0.3944 |
0.1056 |
2.25 |
0.4878 |
0.0122 |
3.25 |
0.4994 |
0.0006 |
|
0.26 |
0.1026 |
0.3974 |
1.26 |
0.3962 |
0.1038 |
2.26 |
0.4881 |
0.0119 |
3.26 |
0.4994 |
0.0006 |
|
0.27 |
0.1064 |
0.3936 |
1.27 |
0.398 |
0.102 |
2.27 |
0.4884 |
0.0116 |
3.27 |
0.4995 |
0.0005 |
|
0.28 |
0.1103 |
0.3897 |
1.28 |
0.3997 |
0.1003 |
2.28 |
0.4887 |
0.0113 |
3.28 |
0.4995 |
0.0005 |
|
0.29 |
0.1141 |
0.3859 |
1.29 |
0.4015 |
0.0985 |
2.29 |
0.489 |
0.011 |
3.29 |
0.4995 |
0.0005 |
|
0.3 |
0.1179 |
0.3821 |
1.3 |
0.4032 |
0.0968 |
2.3 |
0.4893 |
0.0107 |
3.3 |
0.4995 |
0.0005 |
|
0.31 |
0.1217 |
0.3783 |
1.31 |
0.4049 |
0.0951 |
2.31 |
0.4896 |
0.0104 |
3.31 |
0.4995 |
0.0005 |
|
0.32 |
0.1255 |
0.3745 |
1.32 |
0.4066 |
0.0934 |
2.32 |
0.4898 |
0.0102 |
3.32 |
0.4995 |
0.0005 |
|
0.33 |
0.1293 |
0.3707 |
1.33 |
0.4082 |
0.0918 |
2.33 |
0.4901 |
0.0099 |
3.33 |
0.4996 |
0.0004 |
|
0.34 |
0.1331 |
0.3669 |
1.34 |
0.4099 |
0.0901 |
2.34 |
0.4904 |
0.0096 |
3.34 |
0.4996 |
0.0004 |
|
0.35 |
0.1368 |
0.3632 |
1.35 |
0.4115 |
0.0885 |
2.35 |
0.4906 |
0.0094 |
3.35 |
0.4996 |
0.0004 |
|
0.36 |
0.1406 |
0.3594 |
1.36 |
0.4131 |
0.0869 |
2.36 |
0.4909 |
0.0091 |
3.36 |
0.4996 |
0.0004 |
|
0.37 |
0.1443 |
0.3557 |
1.37 |
0.4147 |
0.0853 |
2.37 |
0.4911 |
0.0089 |
3.37 |
0.4996 |
0.0004 |
|
0.38 |
0.148 |
0.352 |
1.38 |
0.4162 |
0.0838 |
2.38 |
0.4913 |
0.0087 |
3.38 |
0.4996 |
0.0004 |
|
0.39 |
0.1517 |
0.3483 |
1.39 |
0.4177 |
0.0823 |
2.39 |
0.4916 |
0.0084 |
3.39 |
0.4997 |
0.0003 |
|
0.4 |
0.1554 |
0.3446 |
1.4 |
0.4192 |
0.0808 |
2.4 |
0.4918 |
0.0082 |
3.4 |
0.4997 |
0.0003 |
|
0.41 |
0.1591 |
0.3409 |
1.41 |
0.4207 |
0.0793 |
2.41 |
0.492 |
0.008 |
3.41 |
0.4997 |
0.0003 |
|
0.42 |
0.1628 |
0.3372 |
1.42 |
0.4222 |
0.0778 |
2.42 |
0.4922 |
0.0078 |
3.42 |
0.4997 |
0.0003 |
|
0.43 |
0.1664 |
0.3336 |
1.43 |
0.4236 |
0.0764 |
2.43 |
0.4925 |
0.0075 |
3.43 |
0.4997 |
0.0003 |
|
0.44 |
0.17 |
0.33 |
1.44 |
0.4251 |
0.0749 |
2.44 |
0.4927 |
0.0073 |
3.44 |
0.4997 |
0.0003 |
|
0.45 |
0.1736 |
0.3264 |
1.45 |
0.4265 |
0.0735 |
2.45 |
0.4929 |
0.0071 |
3.45 |
0.4997 |
0.0003 |
|
0.46 |
0.1772 |
0.3228 |
1.46 |
0.4279 |
0.0721 |
2.46 |
0.4931 |
0.0069 |
3.46 |
0.4997 |
0.0003 |
|
0.47 |
0.1808 |
0.3192 |
1.47 |
0.4292 |
0.0708 |
2.47 |
0.4932 |
0.0068 |
3.47 |
0.4997 |
0.0003 |
|
0.48 |
0.1844 |
0.3156 |
1.48 |
0.4306 |
0.0694 |
2.48 |
0.4934 |
0.0066 |
3.48 |
0.4997 |
0.0003 |
|
0.49 |
0.1879 |
0.3121 |
1.49 |
0.4319 |
0.0681 |
2.49 |
0.4936 |
0.0064 |
3.49 |
0.4998 |
0.0002 |
|
0.5 |
0.1915 |
0.3085 |
1.5 |
0.4332 |
0.0668 |
2.5 |
0.4938 |
0.0062 |
3.5 |
0.4998 |
0.0002 |
|
0.51 |
0.195 |
0.305 |
1.51 |
0.4345 |
0.0655 |
2.51 |
0.494 |
0.006 |
3.51 |
0.4998 |
0.0002 |
|
0.52 |
0.1985 |
0.3015 |
1.52 |
0.4357 |
0.0643 |
2.52 |
0.4941 |
0.0059 |
3.52 |
0.4998 |
0.0002 |
|
0.53 |
0.2019 |
0.2981 |
1.53 |
0.437 |
0.063 |
2.53 |
0.4943 |
0.0057 |
3.53 |
0.4998 |
0.0002 |
|
0.54 |
0.2054 |
0.2946 |
1.54 |
0.4382 |
0.0618 |
2.54 |
0.4945 |
0.0055 |
3.54 |
0.4998 |
0.0002 |
|
0.55 |
0.2088 |
0.2912 |
1.55 |
0.4394 |
0.0606 |
2.55 |
0.4946 |
0.0054 |
3.55 |
0.4998 |
0.0002 |
|
0.56 |
0.2123 |
0.2877 |
1.56 |
0.4406 |
0.0594 |
2.56 |
0.4948 |
0.0052 |
3.56 |
0.4998 |
0.0002 |
|
0.57 |
0.2157 |
0.2843 |
1.57 |
0.4418 |
0.0582 |
2.57 |
0.4949 |
0.0051 |
3.57 |
0.4998 |
0.0002 |
|
0.58 |
0.219 |
0.281 |
1.58 |
0.4429 |
0.0571 |
2.58 |
0.495 |
0.005 |
3.58 |
0.4998 |
0.0002 |
|
0.59 |
0.2224 |
0.2776 |
1.59 |
0.4441 |
0.0559 |
2.59 |
0.4952 |
0.0048 |
3.59 |
0.4998 |
0.0002 |
|
0.6 |
0.2257 |
0.2743 |
1.6 |
0.4452 |
0.0548 |
2.6 |
0.4953 |
0.0047 |
3.6 |
0.4998 |
0.0002 |
|
0.61 |
0.2291 |
0.2709 |
1.61 |
0.4463 |
0.0537 |
2.61 |
0.4955 |
0.0045 |
3.7 |
0.4999 |
0.0001 |
|
0.62 |
0.2324 |
0.2676 |
1.62 |
0.4474 |
0.0526 |
2.62 |
0.4956 |
0.0044 |
|
|
|
|
0.63 |
0.2357 |
0.2643 |
1.63 |
0.4484 |
0.0516 |
2.63 |
0.4957 |
0.0043 |
|
|
|
|
0.64 |
0.2389 |
0.2611 |
1.64 |
0.4495 |
0.0505 |
2.64 |
0.4959 |
0.0041 |
|
|
|
|
0.65 |
0.2422 |
0.2578 |
1.65 |
0.4505 |
0.0495 |
2.65 |
0.496 |
0.004 |
|
|
|
|
0.66 |
0.2454 |
0.2546 |
1.66 |
0.4515 |
0.0485 |
2.66 |
0.4961 |
0.0039 |
|
|
|
|
0.67 |
0.2486 |
0.2514 |
1.67 |
0.4525 |
0.0475 |
2.67 |
0.4962 |
0.0038 |
|
|
|
|
0.68 |
0.2517 |
0.2483 |
1.68 |
0.4535 |
0.0465 |
2.68 |
0.4963 |
0.0037 |
|
|
|
|
0.69 |
0.2549 |
0.2451 |
1.69 |
0.4545 |
0.0455 |
2.69 |
0.4964 |
0.0036 |
|
|
|
|
0.7 |
0.258 |
0.242 |
1.7 |
0.4554 |
0.0446 |
2.7 |
0.4965 |
0.0035 |
|
|
|
|
0.71 |
0.2611 |
0.2389 |
1.71 |
0.4564 |
0.0436 |
2.71 |
0.4966 |
0.0034 |
|
|
|
|
0.72 |
0.2642 |
0.2358 |
1.72 |
0.4573 |
0.0427 |
2.72 |
0.4967 |
0.0033 |
|
|
|
|
0.73 |
0.2673 |
0.2327 |
1.73 |
0.4582 |
0.0418 |
2.73 |
0.4968 |
0.0032 |
|
|
|
|
0.74 |
0.2704 |
0.2296 |
1.74 |
0.4591 |
0.0409 |
2.74 |
0.4969 |
0.0031 |
|
|
|
|
0.75 |
0.2734 |
0.2266 |
1.75 |
0.4599 |
0.0401 |
2.75 |
0.497 |
0.003 |
|
|
|
|
0.76 |
0.2764 |
0.2236 |
1.76 |
0.4608 |
0.0392 |
2.76 |
0.4971 |
0.0029 |
|
|
|
|
0.77 |
0.2794 |
0.2206 |
1.77 |
0.4616 |
0.0384 |
2.77 |
0.4972 |
0.0028 |
|
|
|
|
0.78 |
0.2823 |
0.2177 |
1.78 |
0.4625 |
0.0375 |
2.78 |
0.4973 |
0.0027 |
|
|
|
|
0.79 |
0.2852 |
0.2148 |
1.79 |
0.4633 |
0.0367 |
2.79 |
0.4974 |
0.0026 |
|
|
|
|
0.8 |
0.2881 |
0.2119 |
1.8 |
0.4641 |
0.0359 |
2.8 |
0.4974 |
0.0026 |
|
|
|
|
0.81 |
0.291 |
0.209 |
1.81 |
0.4649 |
0.0351 |
2.81 |
0.4975 |
0.0025 |
|
|
|
|
0.82 |
0.2939 |
0.2061 |
1.82 |
0.4656 |
0.0344 |
2.82 |
0.4976 |
0.0024 |
|
|
|
|
0.83 |
0.2967 |
0.2033 |
1.83 |
0.4664 |
0.0336 |
2.83 |
0.4977 |
0.0023 |
|
|
|
|
0.84 |
0.2995 |
0.2005 |
1.84 |
0.4671 |
0.0329 |
2.84 |
0.4977 |
0.0023 |
|
|
|
|
0.85 |
0.3023 |
0.1977 |
1.85 |
0.4678 |
0.0322 |
2.85 |
0.4978 |
0.0022 |
|
|
|
|
0.86 |
0.3051 |
0.1949 |
1.86 |
0.4686 |
0.0314 |
2.86 |
0.4979 |
0.0021 |
|
|
|
|
0.87 |
0.3078 |
0.1922 |
1.87 |
0.4693 |
0.0307 |
2.87 |
0.4979 |
0.0021 |
|
|
|
|
0.88 |
0.3106 |
0.1894 |
1.88 |
0.4699 |
0.0301 |
2.88 |
0.498 |
0.002 |
|
|
|
|
0.89 |
0.3133 |
0.1867 |
1.89 |
0.4706 |
0.0294 |
2.89 |
0.4981 |
0.0019 |
|
|
|
|
0.9 |
0.3159 |
0.1841 |
1.9 |
0.4713 |
0.0287 |
2.9 |
0.4981 |
0.0019 |
|
|
|
|
0.91 |
0.3186 |
0.1814 |
1.91 |
0.4719 |
0.0281 |
2.91 |
0.4982 |
0.0018 |
|
|
|
|
0.92 |
0.3212 |
0.1788 |
1.92 |
0.4726 |
0.0274 |
2.92 |
0.4982 |
0.0018 |
|
|
|
|
0.93 |
0.3238 |
0.1762 |
1.93 |
0.4732 |
0.0268 |
2.93 |
0.4983 |
0.0017 |
|
|
|
|
0.94 |
0.3264 |
0.1736 |
1.94 |
0.4738 |
0.0262 |
2.94 |
0.4984 |
0.0016 |
|
|
|
|
0.95 |
0.3289 |
0.1711 |
1.95 |
0.4744 |
0.0256 |
2.95 |
0.4984 |
0.0016 |
|
|
|
|
0.96 |
0.3315 |
0.1685 |
1.96 |
0.475 |
0.025 |
2.96 |
0.4985 |
0.0015 |
|
|
|
|
0.97 |
0.334 |
0.166 |
1.97 |
0.4756 |
0.0244 |
2.97 |
0.4985 |
0.0015 |
|
|
|
|
0.98 |
0.3365 |
0.1635 |
1.98 |
0.4761 |
0.0239 |
2.98 |
0.4986 |
0.0014 |
|
|
|
|
0.99 |
0.3389 |
0.1611 |
1.99 |
0.4767 |
0.0233 |
2.99 |
0.4986 |
0.0014 |
|
|
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