Tools
Intervals & Tests
Hypothesis Test Of Sample Mean Example
Hypothesis Test Of Two Sample Variances Example
Hypothesis Test Of A Standard Deviation Compared To A Standard Value Example
Distributions
Area Under the Standard Normal Curve
Non-Normal Distributions in the Real World
Rayleigh Distribution for True Position
z |
0.00 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
–3.4 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0003 |
0.0002 |
–3.3 |
0.0005 |
0.0005 |
0.0005 |
0.0004 |
0.0004 |
0.0004 |
0.0004 |
0.0004 |
0.0004 |
0.0003 |
–3.2 |
0.0007 |
0.0007 |
0.0006 |
0.0006 |
0.0006 |
0.0006 |
0.0006 |
0.0005 |
0.0005 |
0.0005 |
–3.1 |
0.0010 |
0.0009 |
0.0009 |
0.0009 |
0.0008 |
0.0008 |
0.0008 |
0.0008 |
0.0007 |
0.0007 |
–3.0 |
0.0013 |
0.0013 |
0.0013 |
0.0012 |
0.0012 |
0.0011 |
0.0011 |
0.0011 |
0.0010 |
0.0010 |
–2.9 |
0.0019 |
0.0018 |
0.0018 |
0.0017 |
0.0016 |
0.0016 |
0.0015 |
0.0015 |
0.0014 |
0.0014 |
–2.8 |
0.0026 |
0.0025 |
0.0024 |
0.0023 |
0.0023 |
0.0022 |
0.0021 |
0.0021 |
0.0020 |
0.0019 |
–2.7 |
0.0035 |
0.0034 |
0.0033 |
0.0032 |
0.0031 |
0.0030 |
0.0029 |
0.0028 |
0.0027 |
0.0026 |
–2.6 |
0.0047 |
0.0045 |
0.0044 |
0.0043 |
0.0041 |
0.0040 |
0.0039 |
0.0038 |
0.0037 |
0.0036 |
–2.5 |
0.0062 |
0.0060 |
0.0059 |
0.0057 |
0.0055 |
0.0054 |
0.0052 |
0.0051 |
0.0049 |
0.0048 |
–2.4 |
0.0082 |
0.0080 |
0.0078 |
0.0075 |
0.0073 |
0.0071 |
0.0069 |
0.0068 |
0.0066 |
0.0064 |
–2.3 |
0.0107 |
0.0104 |
0.0102 |
0.0090 |
0.0096 |
0.0094 |
0.0091 |
0.0089 |
0.0087 |
0.0084 |
–2.2 |
0.0139 |
0.0136 |
0.0132 |
0.0129 |
0.0125 |
0.0122 |
0.0119 |
0.0116 |
0.0113 |
0.0110 |
–2.1 |
0.0179 |
0.0174 |
0.0170 |
0.0166 |
0.0162 |
0.0158 |
0.0154 |
0.0150 |
0.0146 |
0.0143 |
–2.0 |
0.0228 |
0.0222 |
0.0217 |
0.0212 |
0.0207 |
0.0202 |
0.0197 |
0.0192 |
0.0188 |
0.0183 |
–1.9 |
0.0287 |
0.0281 |
0.0274 |
0.0268 |
0.0262 |
0.0256 |
0.0250 |
0.0244 |
0.0239 |
0.0233 |
–1.8 |
0.0359 |
0.0351 |
0.0344 |
0.0336 |
0.0329 |
0.0322 |
0.0314 |
0.0307 |
0.0301 |
0.0294 |
–1.7 |
0.0446 |
0.0436 |
0.0427 |
0.0418 |
0.0409 |
0.0401 |
0.0392 |
0.0384 |
0.0375 |
0.0367 |
–1.6 |
0.0548 |
0.0537 |
0.0526 |
0.0516 |
0.0505 |
0.0495 |
0.0485 |
0.0475 |
0.0465 |
0.0455 |
–1.5 |
0.0668 |
0.0655 |
0.0643 |
0.0630 |
0.0618 |
0.0606 |
0.0594 |
0.0582 |
0.0571 |
0.0559 |
–1.4 |
0.0808 |
0.0793 |
0.0778 |
0.0764 |
0.0749 |
0.0735 |
0.0721 |
0.0708 |
0.0694 |
0.0681 |
–1.3 |
0.0968 |
0.0951 |
0.0934 |
0.0918 |
0.0901 |
0.0885 |
0.0869 |
0.0853 |
0.0838 |
0.0823 |
–1.2 |
0.1151 |
0.1131 |
0.1112 |
0.1093 |
0.1075 |
0.1056 |
0.1038 |
0.1020 |
0.1003 |
0.0985 |
–1.1 |
0.1357 |
0.1335 |
0.1314 |
0.1292 |
0.1271 |
0.1251 |
0.1230 |
0.1210 |
0.1190 |
0.1170 |
–1.0 |
0.1587 |
0.1562 |
0.1539 |
0.1515 |
0.1492 |
0.1469 |
0.1446 |
0.1423 |
0.1401 |
0.1379 |
–0.9 |
0.1841 |
0.1814 |
0.1788 |
0.1762 |
0.1736 |
0.1711 |
0.1685 |
0.1660 |
0.1635 |
0.1611 |
–0.8 |
0.2119 |
0.2090 |
0.2061 |
0.2033 |
0.2005 |
0.1977 |
0.1949 |
0.1922 |
0.1894 |
0.1867 |
–0.7 |
0.2420 |
0.2389 |
0.2358 |
0.2327 |
0.2296 |
0.2266 |
0.2236 |
0.2206 |
0.2177 |
0.2148 |
–0.6 |
0.2743 |
0.2709 |
0.2676 |
0.2643 |
0.2611 |
0.2578 |
0.2546 |
0.2514 |
0.2483 |
0.2451 |
–0.5 |
0.3085 |
0.3050 |
0.3015 |
0.2981 |
0.2946 |
0.2912 |
0.2877 |
0.2843 |
0.2810 |
0.2776 |
–0.4 |
0.3446 |
0.3409 |
0.3372 |
0.3336 |
0.3300 |
0.3264 |
0.3228 |
0.3192 |
0.3156 |
0.3121 |
–0.3 |
0.3821 |
0.3783 |
0.3745 |
0.3707 |
0.3669 |
0.3632 |
0.3594 |
0.3557 |
0.3520 |
0.3483 |
–0.2 |
0.4207 |
0.4168 |
0.4129 |
0.4090 |
0.4052 |
0.4013 |
0.3974 |
0.3936 |
0.3897 |
0.3859 |
–0.1 |
0.4602 |
0.4562 |
0.4522 |
0.4483 |
0.4443 |
0.4404 |
0.4364 |
0.4325 |
0.4286 |
0.4247 |
–0.0 |
0.5000 |
0.4960 |
0.4920 |
0.4880 |
0.4840 |
0.4801 |
0.4761 |
0.4721 |
0.4681 |
0.4641 |
–0.0 |
0.5000 |
0.5040 |
0.5080 |
0.5120 |
0.5160 |
0.5199 |
0.5239 |
0.5279 |
0.5319 |
0.5359 |
0.1 |
0.5398 |
0.5438 |
0.5478 |
0.5517 |
0.5557 |
0.5596 |
0.5636 |
0.5675 |
0.5714 |
0.5753 |
0.2 |
0.5793 |
0.5832 |
0.5871 |
0.5910 |
0.5948 |
0.5987 |
0.6026 |
0.6064 |
0.6103 |
0.6141 |
0.3 |
0.6179 |
0.6217 |
0.6255 |
0.6293 |
0.6331 |
0.6368 |
0.6406 |
0.6443 |
0.6480 |
0.6517 |
0.4 |
0.6554 |
0.6591 |
0.6628 |
0.6664 |
0.6700 |
0.6736 |
0.6772 |
0.6808 |
0.6844 |
0.6879 |
0.5 |
0.6915 |
0.6950 |
0.6985 |
0.7019 |
0.7054 |
0.7088 |
0.7123 |
0.7157 |
0.7190 |
0.7224 |
0.6 |
0.7257 |
0.7291 |
0.7324 |
0.7357 |
0.7389 |
0.7422 |
0.7454 |
0.7486 |
0.7517 |
0.7549 |
0.7 |
0.7580 |
0.7611 |
0.7642 |
0.7673 |
0.7704 |
0.7734 |
0.7764 |
0.7794 |
0.7823 |
0.7852 |
0.8 |
0.7881 |
0.7910 |
0.7939 |
0.7967 |
0.7995 |
0.8023 |
0.8051 |
0.8078 |
0.8106 |
0.8133 |
0.9 |
0.8159 |
0.8186 |
0.8212 |
0.8238 |
0.8264 |
0.8289 |
0.8315 |
0.8340 |
0.8365 |
0.8389 |
1.0 |
0.8413 |
0.8438 |
0.8461 |
0.8485 |
0.8508 |
0.8531 |
0.8554 |
0.8577 |
0.8599 |
0.8621 |
1.1 |
0.8643 |
0.8665 |
0.8686 |
0.8708 |
0.8729 |
0.8749 |
0.8770 |
0.8790 |
0.8810 |
0.8830 |
1.2 |
0.8849 |
0.8869 |
0.8888 |
0.8907 |
0.8925 |
0.8944 |
0.8962 |
0.8980 |
0.8997 |
0.9015 |
1.3 |
0.9032 |
0.9049 |
0.9066 |
0.9082 |
0.9099 |
0.9115 |
0.9131 |
0.9147 |
0.9162 |
0.9177 |
1.4 |
0.9192 |
0.9207 |
0.9222 |
0.9236 |
0.9251 |
0.9265 |
0.9279 |
0.9292 |
0.9306 |
0.9319 |
1.5 |
0.9332 |
0.9345 |
0.9357 |
0.9370 |
0.9382 |
0.9394 |
0.9406 |
0.9418 |
0.9429 |
0.9441 |
1.6 |
0.9452 |
0.9463 |
0.9474 |
0.9484 |
0.9495 |
0.9505 |
0.9515 |
0.9525 |
0.9535 |
0.9545 |
1.7 |
0.9554 |
0.9564 |
0.9573 |
0.9582 |
0.9591 |
0.9599 |
0.9608 |
0.9616 |
0.9625 |
0.9633 |
1.8 |
0.9641 |
0.9649 |
0.9656 |
0.9664 |
0.9671 |
0.9678 |
0.9686 |
0.9693 |
0.9699 |
0.9706 |
1.9 |
0.9713 |
0.9719 |
0.9726 |
0.9732 |
0.9738 |
0.9744 |
0.9750 |
0.9756 |
0.9761 |
0.9767 |
2.0 |
0.9772 |
0.9778 |
0.9783 |
0.9788 |
0.9793 |
0.9798 |
0.9803 |
0.9808 |
0.9812 |
0.9817 |
2.1 |
0.9821 |
0.9826 |
0.9830 |
0.9834 |
0.9838 |
0.9842 |
0.9846 |
0.9850 |
0.9854 |
0.9857 |
2.2 |
0.9861 |
0.9864 |
0.9868 |
0.9871 |
0.9875 |
0.9878 |
0.9881 |
0.9884 |
0.9887 |
0.9890 |
2.3 |
0.9893 |
0.9896 |
0.9898 |
0.9901 |
0.9904 |
0.9906 |
0.9909 |
0.9911 |
0.9913 |
0.9916 |
2.4 |
0.9918 |
0.9920 |
0.9922 |
0.9925 |
0.9927 |
0.9929 |
0.9931 |
0.9932 |
0.9934 |
0.9936 |
2.5 |
0.9938 |
0.9940 |
0.9941 |
0.9943 |
0.9945 |
0.9946 |
0.9948 |
0.9949 |
0.9951 |
0.9952 |
2.6 |
0.9953 |
0.9955 |
0.9956 |
0.9957 |
0.9959 |
0.9960 |
0.9961 |
0.9962 |
0.9963 |
0.9964 |
2.7 |
0.9965 |
0.9966 |
0.9967 |
0.9968 |
0.9969 |
0.9970 |
0.9971 |
0.9972 |
0.9973 |
0.9974 |
2.8 |
0.9974 |
0.9975 |
0.9976 |
0.9977 |
0.9977 |
0.9978 |
0.9979 |
0.9979 |
0.9980 |
0.9981 |
2.9 |
0.9981 |
0.9982 |
0.9982 |
0.9983 |
0.9984 |
0.9984 |
0.9985 |
0.9985 |
0.9986 |
0.9986 |
3.0 |
0.9987 |
0.9987 |
0.9987 |
0.9988 |
0.9988 |
0.9989 |
0.9989 |
0.9989 |
0.9990 |
0.9990 |
3.1 |
0.9990 |
0.9991 |
0.9991 |
0.9991 |
0.9992 |
0.9992 |
0.9992 |
0.9992 |
0.9993 |
0.9993 |
3.2 |
0.9993 |
0.9993 |
0.9994 |
0.9994 |
0.9994 |
0.9994 |
0.9994 |
0.9995 |
0.9995 |
0.9995 |
3.3 |
0.9995 |
0.9995 |
0.9995 |
0.9996 |
0.9996 |
0.9996 |
0.9996 |
0.9996 |
0.9996 |
0.9997 |
3.4 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9997 |
0.9998 |
Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).