常见概率分布汇总表(可直接打印!)
概率统计分布表(常用)
标准正态表x0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 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 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 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 0.97672.1 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 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 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 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000n\p0.005 0.010 0.025 0.050 0.100 0.250 0.750 0.900 0.950 0.975 0.990 0.9951 0.0000 0.0002 0.0010 0.0039 0.0158 0.1015 1.3233 2.7055 3.8415 5.0239 6.6349 7.87942 0.0100 0.0201 0.0506 0.1026 0.2107 0.5754 2.7726 4.6052 5.9915 7.3778 9.2103 10.59663 0.0717 0.1148 0.2158 0.3518 0.5844 1.2125 4.1083 6.2514 7.8147 9.3484 11.3449 12.83824 0.2070 0.2971 0.4844 0.7107 1.0636 1.9226 5.3853 7.7794 9.4877 11.1433 13.2767 14.86035 0.4117 0.5543 0.8312 1.1455 1.6103 2.6746 6.6257 9.2364 11.0705 12.8325 15.0863 16.74966 0.6757 0.8721 1.2373 1.6354 2.2041 3.4546 7.8408 10.6446 12.5916 14.4494 16.8119 18.54767 0.9893 1.2390 1.6899 2.1673 2.8331 4.2549 9.0371 12.0170 14.0671 16.0128 18.4753 20.27778 1.3444 1.6465 2.1797 2.7326 3.4895 5.0706 10.2189 13.3616 15.5073 17.5345 20.0902 21.95509 1.7349 2.0879 2.7004 3.3251 4.1682 5.8988 11.3888 14.6837 16.9190 19.0228 21.6660 23.589410 2.1559 2.5582 3.2470 3.9403 4.8652 6.7372 12.5489 15.9872 18.3070 20.4832 23.2093 25.188211 2.6032 3.0535 3.8157 4.5748 5.5778 7.5841 13.7007 17.2750 19.6751 21.9200 24.7250 26.756812 3.0738 3.5706 4.4038 5.2260 6.3038 8.4384 14.8454 18.5493 21.0261 23.3367 26.2170 28.299513 3.5650 4.1069 5.0088 5.8919 7.0415 9.2991 15.9839 19.8119 22.3620 24.7356 27.6882 29.819514 4.0747 4.6604 5.6287 6.5706 7.7895 10.1653 17.1169 21.0641 23.6848 26.1189 29.1412 31.319315 4.6009 5.2293 6.2621 7.2609 8.5468 11.0365 18.2451 22.3071 24.9958 27.4884 30.5779 32.801316 5.1422 5.8122 6.9077 7.9616 9.3122 11.9122 19.3689 23.5418 26.2962 28.8454 31.9999 34.267217 5.6972 6.4078 7.5642 8.6718 10.0852 12.7919 20.4887 24.7690 27.5871 30.1910 33.4087 35.718518 6.2648 7.0149 8.2307 9.3905 10.8649 13.6753 21.6049 25.9894 28.8693 31.5264 34.8053 37.156519 6.8440 7.6327 8.9065 10.1170 11.6509 14.5620 22.7178 27.2036 30.1435 32.8523 36.1909 38.582320 7.4338 8.2604 9.5908 10.8508 12.4426 15.4518 23.8277 28.4120 31.4104 34.1696 37.5662 39.996821 8.0337 8.8972 10.2829 11.5913 13.2396 16.3444 24.9348 29.6151 32.6706 35.4789 38.9322 41.401122 8.6427 9.5425 10.9823 12.3380 14.0415 17.2396 26.0393 30.8133 33.9244 36.7807 40.2894 42.795724 9.8862 10.8564 12.4012 13.8484 15.6587 19.0373 28.2412 33.1962 36.4150 39.3641 42.9798 45.558525 10.5197 11.5240 13.1197 14.6114 16.4734 19.9393 29.3389 34.3816 37.6525 40.6465 44.3141 46.927926 11.1602 12.1981 13.8439 15.3792 17.2919 20.8434 30.4346 35.5632 38.8851 41.9232 45.6417 48.289927 11.8076 12.8785 14.5734 16.1514 18.1139 21.7494 31.5284 36.7412 40.1133 43.1945 46.9629 49.644928 12.4613 13.5647 15.3079 16.9279 18.9392 22.6572 32.6205 37.9159 41.3371 44.4608 48.2782 50.993429 13.1211 14.2565 16.0471 17.7084 19.7677 23.5666 33.7109 39.0875 42.5570 45.7223 49.5879 52.335630 13.7867 14.9535 16.7908 18.4927 20.5992 24.4776 34.7997 40.2560 43.7730 46.9792 50.8922 53.672031 14.4578 15.6555 17.5387 19.2806 21.4336 25.3901 35.8871 41.4217 44.9853 48.2319 52.1914 55.002732 15.1340 16.3622 18.2908 20.0719 22.2706 26.3041 36.9730 42.5847 46.1943 49.4804 53.4858 56.328133 15.8153 17.0735 19.0467 20.8665 23.1102 27.2194 38.0575 43.7452 47.3999 50.7251 54.7755 57.648434 16.5013 17.7891 19.8063 21.6643 23.9523 28.1361 39.1408 44.9032 48.6024 51.9660 56.0609 58.963935 17.1918 18.5089 20.5694 22.4650 24.7967 29.0540 40.2228 46.0588 49.8018 53.2033 57.3421 60.274836 17.8867 19.2327 21.3359 23.2686 25.6433 29.9730 41.3036 47.2122 50.9985 54.4373 58.6192 61.581237 18.5858 19.9602 22.1056 24.0749 26.4921 30.8933 42.3833 48.3634 52.1923 55.6680 59.8925 62.883338 19.2889 20.6914 22.8785 24.8839 27.3430 31.8146 43.4619 49.5126 53.3835 56.8955 61.1621 64.181439 19.9959 21.4262 23.6543 25.6954 28.1958 32.7369 44.5395 50.6598 54.5722 58.1201 62.4281 65.475640 20.7065 22.1643 24.4330 26.5093 29.0505 33.6603 45.6160 51.8051 55.7585 59.3417 63.6907 66.766041 21.4208 22.9056 25.2145 27.3256 29.9071 34.5846 46.6916 52.9485 56.9424 60.5606 64.9501 68.052742 22.1385 23.6501 25.9987 28.1440 30.7654 35.5099 47.7663 54.0902 58.1240 61.7768 66.2062 69.336043 22.8595 24.3976 26.7854 28.9647 31.6255 36.4361 48.8400 55.2302 59.3035 62.9904 67.4593 70.615944 23.5837 25.1480 27.5746 29.7875 32.4871 37.3631 49.9129 56.3685 60.4809 64.2015 68.7095 71.892645 24.3110 25.9013 28.3662 30.6123 33.3504 38.2910 50.9849 57.5053 61.6562 65.4102 69.9568 73.1661T分布n\p0.750 0.800 0.850 0.900 0.950 0.975 0.990 0.995 0.9975 0.9990 0.99951 1.0000 1.3764 1.9626 3.0777 6.3138 12.7062 31.8205 63.6567 127.3213 318.3088 636.61922 0.8165 1.0607 1.3862 1.8856 2.9200 4.3027 6.9646 9.9248 14.0890 22.3271 31.59913 0.7649 0.9785 1.2498 1.6377 2.3534 3.1824 4.5407 5.8409 7.4533 10.2145 12.92404 0.7407 0.9410 1.1896 1.5332 2.1318 2.7764 3.7469 4.6041 5.5976 7.1732 8.61035 0.7267 0.9195 1.1558 1.4759 2.0150 2.5706 3.3649 4.0321 4.7733 5.8934 6.86886 0.7176 0.9057 1.1342 1.4398 1.9432 2.4469 3.1427 3.7074 4.3168 5.2076 5.95887 0.7111 0.8960 1.1192 1.4149 1.8946 2.3646 2.9980 3.4995 4.0293 4.7853 5.40798 0.7064 0.8889 1.1081 1.3968 1.8595 2.3060 2.8965 3.3554 3.8325 4.5008 5.04139 0.7027 0.8834 1.0997 1.3830 1.8331 2.2622 2.8214 3.2498 3.6897 4.2968 4.780910 0.6998 0.8791 1.0931 1.3722 1.8125 2.2281 2.7638 3.1693 3.5814 4.1437 4.586911 0.6974 0.8755 1.0877 1.3634 1.7959 2.2010 2.7181 3.1058 3.4966 4.0247 4.437012 0.6955 0.8726 1.0832 1.3562 1.7823 2.1788 2.6810 3.0545 3.4284 3.9296 4.317813 0.6938 0.8702 1.0795 1.3502 1.7709 2.1604 2.6503 3.0123 3.3725 3.8520 4.220814 0.6924 0.8681 1.0763 1.3450 1.7613 2.1448 2.6245 2.9768 3.3257 3.7874 4.140515 0.6912 0.8662 1.0735 1.3406 1.7531 2.1314 2.6025 2.9467 3.2860 3.7328 4.072816 0.6901 0.8647 1.0711 1.3368 1.7459 2.1199 2.5835 2.9208 3.2520 3.6862 4.015017 0.6892 0.8633 1.0690 1.3334 1.7396 2.1098 2.5669 2.8982 3.2224 3.6458 3.965119 0.6876 0.8610 1.0655 1.3277 1.7291 2.0930 2.5395 2.8609 3.1737 3.5794 3.883420 0.6870 0.8600 1.0640 1.3253 1.7247 2.0860 2.5280 2.8453 3.1534 3.5518 3.849521 0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.5176 2.8314 3.1352 3.5272 3.819322 0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.5083 2.8188 3.1188 3.5050 3.792123 0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.4999 2.8073 3.1040 3.4850 3.767624 0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.4922 2.7969 3.0905 3.4668 3.745425 0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.4851 2.7874 3.0782 3.4502 3.725126 0.6840 0.8557 1.0575 1.3150 1.7056 2.0555 2.4786 2.7787 3.0669 3.4350 3.706627 0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.4727 2.7707 3.0565 3.4210 3.689628 0.6834 0.8546 1.0560 1.3125 1.7011 2.0484 2.4671 2.7633 3.0469 3.4082 3.673929 0.6830 0.8542 1.0553 1.3114 1.6991 2.0452 2.4620 2.7564 3.0380 3.3962 3.659430 0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.4573 2.7500 3.0298 3.3852 3.646031 0.6825 0.8534 1.0541 1.3095 1.6955 2.0395 2.4528 2.7440 3.0221 3.3749 3.633532 0.6822 0.8530 1.0535 1.3086 1.6939 2.0369 2.4487 2.7385 3.0149 3.3653 3.621833 0.6820 0.8526 1.0530 1.3077 1.6924 2.0345 2.4448 2.7333 3.0082 3.3563 3.610934 0.6818 0.8523 1.0525 1.3070 1.6909 2.0322 2.4411 2.7284 3.0020 3.3479 3.600735 0.6816 0.8520 1.0520 1.3062 1.6896 2.0301 2.4377 2.7238 2.9960 3.3400 3.591136 0.6814 0.8517 1.0516 1.3055 1.6883 2.0281 2.4345 2.7195 2.9905 3.3326 3.582137 0.6812 0.8514 1.0512 1.3049 1.6871 2.0262 2.4314 2.7154 2.9852 3.3256 3.573738 0.6810 0.8512 1.0508 1.3042 1.6860 2.0244 2.4286 2.7116 2.9803 3.3190 3.565739 0.6808 0.8509 1.0504 1.3036 1.6849 2.0227 2.4258 2.7079 2.9756 3.3128 3.558140 0.6807 0.8507 1.0500 1.3031 1.6839 2.0211 2.4233 2.7045 2.9712 3.3069 3.551041 0.6805 0.8505 1.0497 1.3025 1.6829 2.0195 2.4208 2.7012 2.9670 3.3013 3.544242 0.6804 0.8503 1.0494 1.3020 1.6820 2.0181 2.4185 2.6981 2.9630 3.2960 3.537743 0.6802 0.8501 1.0491 1.3016 1.6811 2.0167 2.4163 2.6951 2.9592 3.2909 3.531644 0.6801 0.8499 1.0488 1.3011 1.6802 2.0154 2.4141 2.6923 2.9555 3.2861 3.525845 0.6800 0.8497 1.0485 1.3006 1.6794 2.0141 2.4121 2.6896 2.9521 3.2815 3.520346 0.6799 0.8495 1.0483 1.3002 1.6787 2.0129 2.4102 2.6870 2.9488 3.2771 3.515047 0.6797 0.8493 1.0480 1.2998 1.6779 2.0117 2.4083 2.6846 2.9456 3.2729 3.509948 0.6796 0.8492 1.0478 1.2994 1.6772 2.0106 2.4066 2.6822 2.9426 3.2689 3.505149 0.6795 0.8490 1.0475 1.2991 1.6766 2.0096 2.4049 2.6800 2.9397 3.2651 3.500450 0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.4033 2.6778 2.9370 3.2614 3.496051 0.6793 0.8487 1.0471 1.2984 1.6753 2.0076 2.4017 2.6757 2.9343 3.2579 3.491853 0.6791 0.8485 1.0467 1.2977 1.6741 2.0057 2.3988 2.6718 2.9293 3.2513 3.483854 0.6791 0.8483 1.0465 1.2974 1.6736 2.0049 2.3974 2.6700 2.9270 3.2481 3.480055 0.6790 0.8482 1.0463 1.2971 1.6730 2.0040 2.3961 2.6682 2.9247 3.2451 3.476456 0.6789 0.8481 1.0461 1.2969 1.6725 2.0032 2.3948 2.6665 2.9225 3.2423 3.472957 0.6788 0.8480 1.0459 1.2966 1.6720 2.0025 2.3936 2.6649 2.9204 3.2395 3.469658 0.6787 0.8479 1.0458 1.2963 1.6716 2.0017 2.3924 2.6633 2.9184 3.2368 3.466359 0.6787 0.8478 1.0456 1.2961 1.6711 2.0010 2.3912 2.6618 2.9164 3.2342 3.463260 0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.3901 2.6603 2.9146 3.2317 3.460261 0.6785 0.8476 1.0453 1.2956 1.6702 1.9996 2.3890 2.6589 2.9127 3.2293 3.457362 0.6785 0.8475 1.0452 1.2954 1.6698 1.9990 2.3880 2.6575 2.9110 3.2270 3.454563 0.6784 0.8474 1.0450 1.2951 1.6694 1.9983 2.3870 2.6561 2.9093 3.2247 3.451864 0.6783 0.8473 1.0449 1.2949 1.6690 1.9977 2.3860 2.6549 2.9076 3.2225 3.449165 0.6783 0.8472 1.0448 1.2947 1.6686 1.9971 2.3851 2.6536 2.9060 3.2204 3.446666 0.6782 0.8471 1.0446 1.2945 1.6683 1.9966 2.3842 2.6524 2.9045 3.2184 3.444167 0.6782 0.8470 1.0445 1.2943 1.6679 1.9960 2.3833 2.6512 2.9030 3.2164 3.441768 0.6781 0.8469 1.0444 1.2941 1.6676 1.9955 2.3824 2.6501 2.9015 3.2145 3.439469 0.6781 0.8469 1.0443 1.2939 1.6672 1.9949 2.3816 2.6490 2.9001 3.2126 3.437270 0.6780 0.8468 1.0442 1.2938 1.6669 1.9944 2.3808 2.6479 2.8987 3.2108 3.435071 0.6780 0.8467 1.0441 1.2936 1.6666 1.9939 2.3800 2.6469 2.8974 3.2090 3.432972 0.6779 0.8466 1.0440 1.2934 1.6663 1.9935 2.3793 2.6459 2.8961 3.2073 3.430873 0.6779 0.8466 1.0438 1.2933 1.6660 1.9930 2.3785 2.6449 2.8949 3.2057 3.428974 0.6778 0.8465 1.0437 1.2931 1.6657 1.9925 2.3778 2.6439 2.8936 3.2041 3.426975 0.6778 0.8464 1.0436 1.2929 1.6654 1.9921 2.3771 2.6430 2.8924 3.2025 3.425076 0.6777 0.8464 1.0436 1.2928 1.6652 1.9917 2.3764 2.6421 2.8913 3.2010 3.423277 0.6777 0.8463 1.0435 1.2926 1.6649 1.9913 2.3758 2.6412 2.8902 3.1995 3.421478 0.6776 0.8463 1.0434 1.2925 1.6646 1.9908 2.3751 2.6403 2.8891 3.1980 3.419779 0.6776 0.8462 1.0433 1.2924 1.6644 1.9905 2.3745 2.6395 2.8880 3.1966 3.418080 0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.3739 2.6387 2.8870 3.1953 3.416381 0.6775 0.8461 1.0431 1.2921 1.6639 1.9897 2.3733 2.6379 2.8860 3.1939 3.414782 0.6775 0.8460 1.0430 1.2920 1.6636 1.9893 2.3727 2.6371 2.8850 3.1926 3.413283 0.6775 0.8460 1.0429 1.2918 1.6634 1.9890 2.3721 2.6364 2.8840 3.1913 3.411684 0.6774 0.8459 1.0429 1.2917 1.6632 1.9886 2.3716 2.6356 2.8831 3.1901 3.410285 0.6774 0.8459 1.0428 1.2916 1.6630 1.9883 2.3710 2.6349 2.8822 3.1889 3.408787 0.6773 0.8458 1.0426 1.2914 1.6626 1.9876 2.3700 2.6335 2.8804 3.1866 3.405988 0.6773 0.8457 1.0426 1.2912 1.6624 1.9873 2.3695 2.6329 2.8795 3.1854 3.404589 0.6773 0.8457 1.0425 1.2911 1.6622 1.9870 2.3690 2.6322 2.8787 3.1843 3.403290 0.6772 0.8456 1.0424 1.2910 1.6620 1.9867 2.3685 2.6316 2.8779 3.1833 3.4019 100 0.6770 0.8452 1.0418 1.2901 1.6602 1.9840 2.3642 2.6259 2.8707 3.1737 3.3905 120 0.6765 0.8446 1.0409 1.2886 1.6577 1.9799 2.3578 2.6174 2.8599 3.1595 3.3735F分布P=0.90n\m 1 2 3 5 6 7 8 10 15 20 301 39.86 49.50 53.59 55.83 57.24 58.91 59.44 59.86 61.22 61.74 62.262 8.53 9.00 9.16 9.24 9.29 9.35 9.37 9.38 9.42 9.44 9.463 5.54 5.46 5.39 5.34 5.31 5.27 5.25 5.24 5.20 5.18 5.174 4.54 4.32 4.19 4.11 4.05 3.98 3.95 3.94 3.87 3.84 3.825 4.06 3.78 3.62 3.52 3.45 3.37 3.34 3.32 3.24 3.21 3.176 3.78 3.46 3.29 3.18 3.11 3.01 2.98 2.96 2.87 2.84 2.807 3.59 3.26 3.07 2.96 2.88 2.78 2.75 2.72 2.63 2.59 2.568 3.46 3.11 2.92 2.81 2.73 2.62 2.59 2.56 2.46 2.42 2.389 3.36 3.01 2.81 2.69 2.61 2.51 2.47 2.44 2.34 2.30 2.2510 3.29 2.92 2.73 2.61 2.52 2.41 2.38 2.35 2.24 2.20 2.1611 3.23 2.86 2.66 2.54 2.45 2.34 2.30 2.27 2.17 2.12 2.0812 3.18 2.81 2.61 2.48 2.39 2.28 2.24 2.21 2.10 2.06 2.0113 3.14 2.76 2.56 2.43 2.35 2.23 2.20 2.16 2.05 2.01 1.9614 3.10 2.73 2.52 2.39 2.31 2.19 2.15 2.12 2.01 1.96 1.9115 3.07 2.70 2.49 2.36 2.27 2.16 2.12 2.09 1.97 1.92 1.8716 3.05 2.67 2.46 2.33 2.24 2.13 2.09 2.06 1.94 1.89 1.8417 3.03 2.64 2.44 2.31 2.22 2.10 2.06 2.03 1.91 1.86 1.8119 2.99 2.61 2.40 2.27 2.18 2.06 2.02 1.98 1.86 1.81 1.7620 2.97 2.59 2.38 2.25 2.16 2.04 2.00 1.96 1.84 1.79 1.7421 2.96 2.57 2.36 2.23 2.14 2.02 1.98 1.95 1.83 1.78 1.7222 2.95 2.56 2.35 2.22 2.13 2.01 1.97 1.93 1.81 1.76 1.7024 2.93 2.54 2.33 2.19 2.10 1.98 1.94 1.91 1.78 1.73 1.6726 2.91 2.52 2.31 2.17 2.08 1.96 1.92 1.88 1.76 1.71 1.6528 2.89 2.50 2.29 2.16 2.06 1.94 1.90 1.87 1.74 1.69 1.6330 2.88 2.49 2.28 2.14 2.05 1.93 1.88 1.85 1.72 1.67 1.61P=0.99n\m 1 2 3 5 6 7 8 10 12 14 16 18 201 4052.18 4999.50 5403.35 5624.58 5763.65 5928.36 5981.07 6022.47 6106.32 6142.67 6170.10 6191.53 6208.732 98.50 99.00 99.17 99.25 99.30 99.36 99.37 99.39 99.42 99.43 99.44 99.44 99.453 34.12 30.82 29.46 28.71 28.24 27.67 27.49 27.35 27.05 26.92 26.83 26.75 26.694 21.20 18.00 16.69 15.98 15.52 14.98 14.80 14.66 14.37 14.25 14.15 14.08 14.025 16.26 13.27 12.06 11.39 10.97 10.46 10.29 10.16 9.89 9.77 9.68 9.61 9.556 13.75 10.92 9.78 9.15 8.75 8.26 8.10 7.98 7.72 7.60 7.52 7.45 7.407 12.25 9.55 8.45 7.85 7.46 6.99 6.84 6.72 6.47 6.36 6.28 6.21 6.168 11.26 8.65 7.59 7.01 6.63 6.18 6.03 5.91 5.67 5.56 5.48 5.41 5.369 10.56 8.02 6.99 6.42 6.06 5.61 5.47 5.35 5.11 5.01 4.92 4.86 4.8111 9.65 7.21 6.22 5.67 5.32 4.89 4.74 4.63 4.40 4.29 4.21 4.15 4.1012 9.33 6.93 5.95 5.41 5.06 4.64 4.50 4.39 4.16 4.05 3.97 3.91 3.8613 9.07 6.70 5.74 5.21 4.86 4.44 4.30 4.19 3.96 3.86 3.78 3.72 3.6614 8.86 6.51 5.56 5.04 4.69 4.28 4.14 4.03 3.80 3.70 3.62 3.56 3.5115 8.68 6.36 5.42 4.89 4.56 4.14 4.00 3.89 3.67 3.56 3.49 3.42 3.3716 8.53 6.23 5.29 4.77 4.44 4.03 3.89 3.78 3.55 3.45 3.37 3.31 3.2617 8.40 6.11 5.18 4.67 4.34 3.93 3.79 3.68 3.46 3.35 3.27 3.21 3.1618 8.29 6.01 5.09 4.58 4.25 3.84 3.71 3.60 3.37 3.27 3.19 3.13 3.0819 8.18 5.93 5.01 4.50 4.17 3.77 3.63 3.52 3.30 3.19 3.12 3.05 3.0020 8.10 5.85 4.94 4.43 4.10 3.70 3.56 3.46 3.23 3.13 3.05 2.99 2.9421 8.02 5.78 4.87 4.37 4.04 3.64 3.51 3.40 3.17 3.07 2.99 2.93 2.8822 7.95 5.72 4.82 4.31 3.99 3.59 3.45 3.35 3.12 3.02 2.94 2.88 2.8323 7.88 5.66 4.76 4.26 3.94 3.54 3.41 3.30 3.07 2.97 2.89 2.83 2.7824 7.82 5.61 4.72 4.22 3.90 3.50 3.36 3.26 3.03 2.93 2.85 2.79 2.7425 7.77 5.57 4.68 4.18 3.85 3.46 3.32 3.22 2.99 2.89 2.81 2.75 2.7026 7.72 5.53 4.64 4.14 3.82 3.42 3.29 3.18 2.96 2.86 2.78 2.72 2.6628 7.64 5.45 4.57 4.07 3.75 3.36 3.23 3.12 2.90 2.79 2.72 2.65 2.6029 7.60 5.42 4.54 4.04 3.73 3.33 3.20 3.09 2.87 2.77 2.69 2.63 2.5730 7.56 5.39 4.51 4.02 3.70 3.30 3.17 3.07 2.84 2.74 2.66 2.60 2.55Excel公式1.正态分布函数Excel计算正态分布时，使用NORMDIST函数，其格式如下：NORMDIST（a，μ，σ，累积）其中，“累积”：若为TRUE，则输出分布函数值，即P{X≤a}；若为FALSE，则为概率密度函数值．示例：已知X服从正态分布，μ＝600，σ＝100，求P{X≤500}．输入公式NORMDIST(500, 600, 100, TRUE)得到的结果为0.158655，即P{X≤500}=0.158655．2、正态分布函数的反函数Excel计算正态分布函数的反函数使用NORMINV函数，格式如下：NORMINV（p，μ，σ），此公式计算a，使P{X ≤a}=p3标准正态分布反函数=NORMSINV(0.975)3、t分布Excel计算t分布的值,采用TDIST函数，格式如下：TDIST（a，自由度，侧数）其中，“侧数”：指明分布为单侧或双侧：若为1，为单侧；此命令输出P{ T >a }若为2，为双侧．此命令输出P{ |T| >a}示例：设T服从自由度为24的t分布，求P(T>1.711)．已知t＝1.711，df=24，采用单侧，则T分布的值：TDIST(1.711,24,1)得到0.05，即P(T > 1.711)=0.05．4. t分布的反函数Excel使用TINV函数得到t分布的反函数，格式如下：TINV（α，自由度）输出T 分布的α / 2 分位点：t_α/2_(n)若求临界值tα(n)，则使用公式＝TINV(2*α, n)5.返回F分布的函数是FDISTFDIST(x,degrees_freedom1,degrees_freedom2)函数FDIST 的计算公式为FDIST=P( F>x )，5.F分布的反函数FINV(probability,deg_freedom1,deg_freedom2)已知probability=P( F>x )，求x。
概率统计分布表格(常用)
标准正态表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 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 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 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 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 0.98572.2 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 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 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 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.99993.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.00009 1.7349 2.0879 2.7004 3.3251 4.1682 5.8988 11.3888 14.6837 16.9190 19.0228 21.6660 23.589410 2.1559 2.5582 3.2470 3.9403 4.8652 6.7372 12.5489 15.9872 18.3070 20.4832 23.2093 25.188211 2.6032 3.0535 3.8157 4.5748 5.5778 7.5841 13.7007 17.2750 19.6751 21.9200 24.7250 26.756812 3.0738 3.5706 4.4038 5.2260 6.3038 8.4384 14.8454 18.5493 21.0261 23.3367 26.2170 28.299513 3.5650 4.1069 5.0088 5.8919 7.0415 9.2991 15.9839 19.8119 22.3620 24.7356 27.6882 29.819514 4.0747 4.6604 5.6287 6.5706 7.7895 10.1653 17.1169 21.0641 23.6848 26.1189 29.1412 31.319315 4.6009 5.2293 6.2621 7.2609 8.5468 11.0365 18.2451 22.3071 24.9958 27.4884 30.5779 32.801316 5.1422 5.8122 6.9077 7.9616 9.3122 11.9122 19.3689 23.5418 26.2962 28.8454 31.9999 34.267217 5.6972 6.4078 7.5642 8.6718 10.0852 12.7919 20.4887 24.7690 27.5871 30.1910 33.4087 35.718518 6.2648 7.0149 8.2307 9.3905 10.8649 13.6753 21.6049 25.9894 28.8693 31.5264 34.8053 37.156519 6.8440 7.6327 8.9065 10.1170 11.6509 14.5620 22.7178 27.2036 30.1435 32.8523 36.1909 38.582320 7.4338 8.2604 9.5908 10.8508 12.4426 15.4518 23.8277 28.4120 31.4104 34.1696 37.5662 39.996821 8.0337 8.8972 10.2829 11.5913 13.2396 16.3444 24.9348 29.6151 32.6706 35.4789 38.9322 41.401122 8.6427 9.5425 10.9823 12.3380 14.0415 17.2396 26.0393 30.8133 33.9244 36.7807 40.2894 42.795723 9.2604 10.1957 11.6886 13.0905 14.8480 18.1373 27.1413 32.0069 35.1725 38.0756 41.6384 44.181324 9.8862 10.8564 12.4012 13.8484 15.6587 19.0373 28.2412 33.1962 36.4150 39.3641 42.9798 45.558525 10.5197 11.5240 13.1197 14.6114 16.4734 19.9393 29.3389 34.3816 37.6525 40.6465 44.3141 46.927926 11.1602 12.1981 13.8439 15.3792 17.2919 20.8434 30.4346 35.5632 38.8851 41.9232 45.6417 48.289927 11.8076 12.8785 14.5734 16.1514 18.1139 21.7494 31.5284 36.7412 40.1133 43.1945 46.9629 49.644928 12.4613 13.5647 15.3079 16.9279 18.9392 22.6572 32.6205 37.9159 41.3371 44.4608 48.2782 50.993429 13.1211 14.2565 16.0471 17.7084 19.7677 23.5666 33.7109 39.0875 42.5570 45.7223 49.5879 52.335630 13.7867 14.9535 16.7908 18.4927 20.5992 24.4776 34.7997 40.2560 43.7730 46.9792 50.8922 53.672031 14.4578 15.6555 17.5387 19.2806 21.4336 25.3901 35.8871 41.4217 44.9853 48.2319 52.1914 55.002732 15.1340 16.3622 18.2908 20.0719 22.2706 26.3041 36.9730 42.5847 46.1943 49.4804 53.4858 56.328133 15.8153 17.0735 19.0467 20.8665 23.1102 27.2194 38.0575 43.7452 47.3999 50.7251 54.7755 57.648434 16.5013 17.7891 19.8063 21.6643 23.9523 28.1361 39.1408 44.9032 48.6024 51.9660 56.0609 58.963935 17.1918 18.5089 20.5694 22.4650 24.7967 29.0540 40.2228 46.0588 49.8018 53.2033 57.3421 60.274836 17.8867 19.2327 21.3359 23.2686 25.6433 29.9730 41.3036 47.2122 50.9985 54.4373 58.6192 61.581237 18.5858 19.9602 22.1056 24.0749 26.4921 30.8933 42.3833 48.3634 52.1923 55.6680 59.8925 62.883338 19.2889 20.6914 22.8785 24.8839 27.3430 31.8146 43.4619 49.5126 53.3835 56.8955 61.1621 64.181439 19.9959 21.4262 23.6543 25.6954 28.1958 32.7369 44.5395 50.6598 54.5722 58.1201 62.4281 65.475640 20.7065 22.1643 24.4330 26.5093 29.0505 33.6603 45.6160 51.8051 55.7585 59.3417 63.6907 66.766041 21.4208 22.9056 25.2145 27.3256 29.9071 34.5846 46.6916 52.9485 56.9424 60.5606 64.9501 68.052742 22.1385 23.6501 25.9987 28.1440 30.7654 35.5099 47.7663 54.0902 58.1240 61.7768 66.2062 69.336043 22.8595 24.3976 26.7854 28.9647 31.6255 36.4361 48.8400 55.2302 59.3035 62.9904 67.4593 70.615944 23.5837 25.1480 27.5746 29.7875 32.4871 37.3631 49.9129 56.3685 60.4809 64.2015 68.7095 71.892645 24.3110 25.9013 28.3662 30.6123 33.3504 38.2910 50.9849 57.5053 61.6562 65.4102 69.9568 73.1661T分布1 1.0000 1.3764 1.9626 3.0777 6.3138 12.7062 31.8205 63.6567 127.3213 318.3088 636.61922 0.8165 1.0607 1.3862 1.8856 2.9200 4.3027 6.9646 9.9248 14.0890 22.3271 31.59913 0.7649 0.9785 1.2498 1.6377 2.3534 3.1824 4.5407 5.8409 7.4533 10.2145 12.92404 0.7407 0.9410 1.1896 1.5332 2.1318 2.7764 3.7469 4.6041 5.5976 7.1732 8.61035 0.7267 0.9195 1.1558 1.4759 2.0150 2.5706 3.3649 4.0321 4.7733 5.8934 6.86886 0.7176 0.9057 1.1342 1.4398 1.9432 2.4469 3.1427 3.7074 4.3168 5.2076 5.95887 0.7111 0.8960 1.1192 1.4149 1.8946 2.3646 2.9980 3.4995 4.0293 4.7853 5.40798 0.7064 0.8889 1.1081 1.3968 1.8595 2.3060 2.8965 3.3554 3.8325 4.5008 5.04139 0.7027 0.8834 1.0997 1.3830 1.8331 2.2622 2.8214 3.2498 3.6897 4.2968 4.780910 0.6998 0.8791 1.0931 1.3722 1.8125 2.2281 2.7638 3.1693 3.5814 4.1437 4.586911 0.6974 0.8755 1.0877 1.3634 1.7959 2.2010 2.7181 3.1058 3.4966 4.0247 4.437012 0.6955 0.8726 1.0832 1.3562 1.7823 2.1788 2.6810 3.0545 3.4284 3.9296 4.317813 0.6938 0.8702 1.0795 1.3502 1.7709 2.1604 2.6503 3.0123 3.3725 3.8520 4.220814 0.6924 0.8681 1.0763 1.3450 1.7613 2.1448 2.6245 2.9768 3.3257 3.7874 4.140515 0.6912 0.8662 1.0735 1.3406 1.7531 2.1314 2.6025 2.9467 3.2860 3.7328 4.072816 0.6901 0.8647 1.0711 1.3368 1.7459 2.1199 2.5835 2.9208 3.2520 3.6862 4.015017 0.6892 0.8633 1.0690 1.3334 1.7396 2.1098 2.5669 2.8982 3.2224 3.6458 3.965118 0.6884 0.8620 1.0672 1.3304 1.7341 2.1009 2.5524 2.8784 3.1966 3.6105 3.921619 0.6876 0.8610 1.0655 1.3277 1.7291 2.0930 2.5395 2.8609 3.1737 3.5794 3.883420 0.6870 0.8600 1.0640 1.3253 1.7247 2.0860 2.5280 2.8453 3.1534 3.5518 3.849521 0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.5176 2.8314 3.1352 3.5272 3.819322 0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.5083 2.8188 3.1188 3.5050 3.792123 0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.4999 2.8073 3.1040 3.4850 3.767624 0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.4922 2.7969 3.0905 3.4668 3.745425 0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.4851 2.7874 3.0782 3.4502 3.725126 0.6840 0.8557 1.0575 1.3150 1.7056 2.0555 2.4786 2.7787 3.0669 3.4350 3.706627 0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.4727 2.7707 3.0565 3.4210 3.689628 0.6834 0.8546 1.0560 1.3125 1.7011 2.0484 2.4671 2.7633 3.0469 3.4082 3.673929 0.6830 0.8542 1.0553 1.3114 1.6991 2.0452 2.4620 2.7564 3.0380 3.3962 3.659430 0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.4573 2.7500 3.0298 3.3852 3.646031 0.6825 0.8534 1.0541 1.3095 1.6955 2.0395 2.4528 2.7440 3.0221 3.3749 3.633532 0.6822 0.8530 1.0535 1.3086 1.6939 2.0369 2.4487 2.7385 3.0149 3.3653 3.621833 0.6820 0.8526 1.0530 1.3077 1.6924 2.0345 2.4448 2.7333 3.0082 3.3563 3.610934 0.6818 0.8523 1.0525 1.3070 1.6909 2.0322 2.4411 2.7284 3.0020 3.3479 3.600735 0.6816 0.8520 1.0520 1.3062 1.6896 2.0301 2.4377 2.7238 2.9960 3.3400 3.591136 0.6814 0.8517 1.0516 1.3055 1.6883 2.0281 2.4345 2.7195 2.9905 3.3326 3.582137 0.6812 0.8514 1.0512 1.3049 1.6871 2.0262 2.4314 2.7154 2.9852 3.3256 3.573738 0.6810 0.8512 1.0508 1.3042 1.6860 2.0244 2.4286 2.7116 2.9803 3.3190 3.565739 0.6808 0.8509 1.0504 1.3036 1.6849 2.0227 2.4258 2.7079 2.9756 3.3128 3.558140 0.6807 0.8507 1.0500 1.3031 1.6839 2.0211 2.4233 2.7045 2.9712 3.3069 3.551041 0.6805 0.8505 1.0497 1.3025 1.6829 2.0195 2.4208 2.7012 2.9670 3.3013 3.544242 0.6804 0.8503 1.0494 1.3020 1.6820 2.0181 2.4185 2.6981 2.9630 3.2960 3.537743 0.6802 0.8501 1.0491 1.3016 1.6811 2.0167 2.4163 2.6951 2.9592 3.2909 3.531644 0.6801 0.8499 1.0488 1.3011 1.6802 2.0154 2.4141 2.6923 2.9555 3.2861 3.525845 0.6800 0.8497 1.0485 1.3006 1.6794 2.0141 2.4121 2.6896 2.9521 3.2815 3.520346 0.6799 0.8495 1.0483 1.3002 1.6787 2.0129 2.4102 2.6870 2.9488 3.2771 3.515047 0.6797 0.8493 1.0480 1.2998 1.6779 2.0117 2.4083 2.6846 2.9456 3.2729 3.509948 0.6796 0.8492 1.0478 1.2994 1.6772 2.0106 2.4066 2.6822 2.9426 3.2689 3.505149 0.6795 0.8490 1.0475 1.2991 1.6766 2.0096 2.4049 2.6800 2.9397 3.2651 3.500450 0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.4033 2.6778 2.9370 3.2614 3.496051 0.6793 0.8487 1.0471 1.2984 1.6753 2.0076 2.4017 2.6757 2.9343 3.2579 3.491852 0.6792 0.8486 1.0469 1.2980 1.6747 2.0066 2.4002 2.6737 2.9318 3.2545 3.487753 0.6791 0.8485 1.0467 1.2977 1.6741 2.0057 2.3988 2.6718 2.9293 3.2513 3.483854 0.6791 0.8483 1.0465 1.2974 1.6736 2.0049 2.3974 2.6700 2.9270 3.2481 3.480055 0.6790 0.8482 1.0463 1.2971 1.6730 2.0040 2.3961 2.6682 2.9247 3.2451 3.476456 0.6789 0.8481 1.0461 1.2969 1.6725 2.0032 2.3948 2.6665 2.9225 3.2423 3.472957 0.6788 0.8480 1.0459 1.2966 1.6720 2.0025 2.3936 2.6649 2.9204 3.2395 3.469658 0.6787 0.8479 1.0458 1.2963 1.6716 2.0017 2.3924 2.6633 2.9184 3.2368 3.466359 0.6787 0.8478 1.0456 1.2961 1.6711 2.0010 2.3912 2.6618 2.9164 3.2342 3.463260 0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.3901 2.6603 2.9146 3.2317 3.460261 0.6785 0.8476 1.0453 1.2956 1.6702 1.9996 2.3890 2.6589 2.9127 3.2293 3.457362 0.6785 0.8475 1.0452 1.2954 1.6698 1.9990 2.3880 2.6575 2.9110 3.2270 3.454563 0.6784 0.8474 1.0450 1.2951 1.6694 1.9983 2.3870 2.6561 2.9093 3.2247 3.451864 0.6783 0.8473 1.0449 1.2949 1.6690 1.9977 2.3860 2.6549 2.9076 3.2225 3.449165 0.6783 0.8472 1.0448 1.2947 1.6686 1.9971 2.3851 2.6536 2.9060 3.2204 3.446666 0.6782 0.8471 1.0446 1.2945 1.6683 1.9966 2.3842 2.6524 2.9045 3.2184 3.444167 0.6782 0.8470 1.0445 1.2943 1.6679 1.9960 2.3833 2.6512 2.9030 3.2164 3.441768 0.6781 0.8469 1.0444 1.2941 1.6676 1.9955 2.3824 2.6501 2.9015 3.2145 3.439469 0.6781 0.8469 1.0443 1.2939 1.6672 1.9949 2.3816 2.6490 2.9001 3.2126 3.437270 0.6780 0.8468 1.0442 1.2938 1.6669 1.9944 2.3808 2.6479 2.8987 3.2108 3.435071 0.6780 0.8467 1.0441 1.2936 1.6666 1.9939 2.3800 2.6469 2.8974 3.2090 3.432972 0.6779 0.8466 1.0440 1.2934 1.6663 1.9935 2.3793 2.6459 2.8961 3.2073 3.430873 0.6779 0.8466 1.0438 1.2933 1.6660 1.9930 2.3785 2.6449 2.8949 3.2057 3.428974 0.6778 0.8465 1.0437 1.2931 1.6657 1.9925 2.3778 2.6439 2.8936 3.2041 3.426975 0.6778 0.8464 1.0436 1.2929 1.6654 1.9921 2.3771 2.6430 2.8924 3.2025 3.425076 0.6777 0.8464 1.0436 1.2928 1.6652 1.9917 2.3764 2.6421 2.8913 3.2010 3.423277 0.6777 0.8463 1.0435 1.2926 1.6649 1.9913 2.3758 2.6412 2.8902 3.1995 3.421478 0.6776 0.8463 1.0434 1.2925 1.6646 1.9908 2.3751 2.6403 2.8891 3.1980 3.419779 0.6776 0.8462 1.0433 1.2924 1.6644 1.9905 2.3745 2.6395 2.8880 3.1966 3.418080 0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.3739 2.6387 2.8870 3.1953 3.416381 0.6775 0.8461 1.0431 1.2921 1.6639 1.9897 2.3733 2.6379 2.8860 3.1939 3.414782 0.6775 0.8460 1.0430 1.2920 1.6636 1.9893 2.3727 2.6371 2.8850 3.1926 3.413283 0.6775 0.8460 1.0429 1.2918 1.6634 1.9890 2.3721 2.6364 2.8840 3.1913 3.411684 0.6774 0.8459 1.0429 1.2917 1.6632 1.9886 2.3716 2.6356 2.8831 3.1901 3.410285 0.6774 0.8459 1.0428 1.2916 1.6630 1.9883 2.3710 2.6349 2.8822 3.1889 3.408786 0.6774 0.8458 1.0427 1.2915 1.6628 1.9879 2.3705 2.6342 2.8813 3.1877 3.407387 0.6773 0.8458 1.0426 1.2914 1.6626 1.9876 2.3700 2.6335 2.8804 3.1866 3.405988 0.6773 0.8457 1.0426 1.2912 1.6624 1.9873 2.3695 2.6329 2.8795 3.1854 3.404589 0.6773 0.8457 1.0425 1.2911 1.6622 1.9870 2.3690 2.6322 2.8787 3.1843 3.403290 0.6772 0.8456 1.0424 1.2910 1.6620 1.9867 2.3685 2.6316 2.8779 3.1833 3.4019 100 0.6770 0.8452 1.0418 1.2901 1.6602 1.9840 2.3642 2.6259 2.8707 3.1737 3.3905 120 0.6765 0.8446 1.0409 1.2886 1.6577 1.9799 2.3578 2.6174 2.8599 3.1595 3.3735F分布P= 0.9011 3.23 2.86 2.66 2.54 2.45 2.34 2.30 2.27 2.17 2.12 2.0812 3.18 2.81 2.61 2.48 2.39 2.28 2.24 2.21 2.10 2.06 2.0113 3.14 2.76 2.56 2.43 2.35 2.23 2.20 2.16 2.05 2.01 1.9614 3.10 2.73 2.52 2.39 2.31 2.19 2.15 2.12 2.01 1.96 1.9115 3.07 2.70 2.49 2.36 2.27 2.16 2.12 2.09 1.97 1.92 1.8716 3.05 2.67 2.46 2.33 2.24 2.13 2.09 2.06 1.94 1.89 1.8417 3.03 2.64 2.44 2.31 2.22 2.10 2.06 2.03 1.91 1.86 1.8118 3.01 2.62 2.42 2.29 2.20 2.08 2.04 2.00 1.89 1.84 1.7819 2.99 2.61 2.40 2.27 2.18 2.06 2.02 1.98 1.86 1.81 1.7620 2.97 2.59 2.38 2.25 2.16 2.04 2.00 1.96 1.84 1.79 1.7421 2.96 2.57 2.36 2.23 2.14 2.02 1.98 1.95 1.83 1.78 1.7222 2.95 2.56 2.35 2.22 2.13 2.01 1.97 1.93 1.81 1.76 1.70 24 2.93 2.54 2.33 2.19 2.10 1.98 1.94 1.91 1.78 1.73 1.67 26 2.91 2.52 2.31 2.17 2.08 1.96 1.92 1.88 1.76 1.71 1.65 28 2.89 2.50 2.29 2.16 2.06 1.94 1.90 1.87 1.74 1.69 1.63 30 2.88 2.49 2.28 2.14 2.05 1.93 1.88 1.85 1.72 1.67 1.61P= 0.9911 9.65 7.21 6.22 5.67 5.32 4.89 4.74 4.63 4.40 4.29 4.21 4.15 4.1012 9.33 6.93 5.95 5.41 5.06 4.64 4.50 4.39 4.16 4.05 3.97 3.91 3.8613 9.07 6.70 5.74 5.21 4.86 4.44 4.30 4.19 3.96 3.86 3.78 3.72 3.6614 8.86 6.51 5.56 5.04 4.69 4.28 4.14 4.03 3.80 3.70 3.62 3.56 3.5115 8.68 6.36 5.42 4.89 4.56 4.14 4.00 3.89 3.67 3.56 3.49 3.42 3.3716 8.53 6.23 5.29 4.77 4.44 4.03 3.89 3.78 3.55 3.45 3.37 3.31 3.2617 8.40 6.11 5.18 4.67 4.34 3.93 3.79 3.68 3.46 3.35 3.27 3.21 3.1618 8.29 6.01 5.09 4.58 4.25 3.84 3.71 3.60 3.37 3.27 3.19 3.13 3.0819 8.18 5.93 5.01 4.50 4.17 3.77 3.63 3.52 3.30 3.19 3.12 3.05 3.0020 8.10 5.85 4.94 4.43 4.10 3.70 3.56 3.46 3.23 3.13 3.05 2.99 2.9421 8.02 5.78 4.87 4.37 4.04 3.64 3.51 3.40 3.17 3.07 2.99 2.93 2.8822 7.95 5.72 4.82 4.31 3.99 3.59 3.45 3.35 3.12 3.02 2.94 2.88 2.8323 7.88 5.66 4.76 4.26 3.94 3.54 3.41 3.30 3.07 2.97 2.89 2.83 2.7824 7.82 5.61 4.72 4.22 3.90 3.50 3.36 3.26 3.03 2.93 2.85 2.79 2.7425 7.77 5.57 4.68 4.18 3.85 3.46 3.32 3.22 2.99 2.89 2.81 2.75 2.7026 7.72 5.53 4.64 4.14 3.82 3.42 3.29 3.18 2.96 2.86 2.78 2.72 2.6627 7.68 5.49 4.60 4.11 3.78 3.39 3.26 3.15 2.93 2.82 2.75 2.68 2.6328 7.64 5.45 4.57 4.07 3.75 3.36 3.23 3.12 2.90 2.79 2.72 2.65 2.6029 7.60 5.42 4.54 4.04 3.73 3.33 3.20 3.09 2.87 2.77 2.69 2.63 2.5730 7.56 5.39 4.51 4.02 3.70 3.30 3.17 3.07 2.84 2.74 2.66 2.60 2.55Excel公式1.正态分布函数Excel计算正态分布时，使用NORMDIST函数，其格式如下：NORMDIST（a，μ，σ，累积）其中，“累积”：若为TRUE，则输出分布函数值，即P{X≤a}；若为FALSE，则为概率密度函数值．示例：已知X服从正态分布，μ＝600，σ＝100，求P{X≤500}．输入公式NORMDIST(500, 600, 100, TRUE)得到的结果为0.158655，即P{X≤500}=0.158655．2、正态分布函数的反函数Excel计算正态分布函数的反函数使用NORMINV函数，格式如下： NORMINV（p，μ，σ），此公式计算a，使P{X ≤a}=p 3标准正态分布反函数=NORMSINV(0.975)3、 t分布Excel计算t分布的值,采用TDIST函数，格式如下： TDIST（a，自由度，侧数）其中，“侧数”：指明分布为单侧或双侧：若为1，为单侧；此命令输出P{ T >a }若为2，为双侧．此命令输出P{ |T| >a}示例：设T服从自由度为24的t分布，求P(T>1.711)．已知t＝1.711，df=24，采用单侧，则T分布的值：TDIST(1.711,24,1)得到0.05，即P(T > 1.711)=0.05．4. t分布的反函数Excel使用TINV函数得到t分布的反函数，格式如下： TINV（α，自由度）输出 T 分布的α / 2 分位点： t_α/2_(n)若求临界值tα(n)，则使用公式＝TINV(2*α, n)5.返回F分布的函数是FDISTFDIST(x,degrees_freedom1,degrees_freedom2) 函数 FDIST 的计算公式为 FDIST=P( F>x )，5.F分布的反函数FINV(probability,deg_freedom1,deg_freedom2) 已知 probability=P( F>x )，求x。
概率统计分布表(常用)
标准正态表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 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 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 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000024 9.8862 10.8564 12.4012 13.8484 15.6587 19.0373 28.2412 33.1962 36.4150 39.3641 42.9798 45.558525 10.5197 11.5240 13.1197 14.6114 16.4734 19.9393 29.3389 34.3816 37.6525 40.6465 44.3141 46.927926 11.1602 12.1981 13.8439 15.3792 17.2919 20.8434 30.4346 35.5632 38.8851 41.9232 45.6417 48.289927 11.8076 12.8785 14.5734 16.1514 18.1139 21.7494 31.5284 36.7412 40.1133 43.1945 46.9629 49.644928 12.4613 13.5647 15.3079 16.9279 18.9392 22.6572 32.6205 37.9159 41.3371 44.4608 48.2782 50.993429 13.1211 14.2565 16.0471 17.7084 19.7677 23.5666 33.7109 39.0875 42.5570 45.7223 49.5879 52.335630 13.7867 14.9535 16.7908 18.4927 20.5992 24.4776 34.7997 40.2560 43.7730 46.9792 50.8922 53.672031 14.4578 15.6555 17.5387 19.2806 21.4336 25.3901 35.8871 41.4217 44.9853 48.2319 52.1914 55.002732 15.1340 16.3622 18.2908 20.0719 22.2706 26.3041 36.9730 42.5847 46.1943 49.4804 53.4858 56.328133 15.8153 17.0735 19.0467 20.8665 23.1102 27.2194 38.0575 43.7452 47.3999 50.7251 54.7755 57.648434 16.5013 17.7891 19.8063 21.6643 23.9523 28.1361 39.1408 44.9032 48.6024 51.9660 56.0609 58.963935 17.1918 18.5089 20.5694 22.4650 24.7967 29.0540 40.2228 46.0588 49.8018 53.2033 57.3421 60.274836 17.8867 19.2327 21.3359 23.2686 25.6433 29.9730 41.3036 47.2122 50.9985 54.4373 58.6192 61.581237 18.5858 19.9602 22.1056 24.0749 26.4921 30.8933 42.3833 48.3634 52.1923 55.6680 59.8925 62.883338 19.2889 20.6914 22.8785 24.8839 27.3430 31.8146 43.4619 49.5126 53.3835 56.8955 61.1621 64.181439 19.9959 21.4262 23.6543 25.6954 28.1958 32.7369 44.5395 50.6598 54.5722 58.1201 62.4281 65.475640 20.7065 22.1643 24.4330 26.5093 29.0505 33.6603 45.6160 51.8051 55.7585 59.3417 63.6907 66.766041 21.4208 22.9056 25.2145 27.3256 29.9071 34.5846 46.6916 52.9485 56.9424 60.5606 64.9501 68.052742 22.1385 23.6501 25.9987 28.1440 30.7654 35.5099 47.7663 54.0902 58.1240 61.7768 66.2062 69.336043 22.8595 24.3976 26.7854 28.9647 31.6255 36.4361 48.8400 55.2302 59.3035 62.9904 67.4593 70.615944 23.5837 25.1480 27.5746 29.7875 32.4871 37.3631 49.9129 56.3685 60.4809 64.2015 68.7095 71.892645 24.3110 25.9013 28.3662 30.6123 33.3504 38.2910 50.9849 57.5053 61.6562 65.4102 69.9568 73.1661T分布n\p 0.750 0.800 0.850 0.900 0.950 0.975 0.990 0.995 0.9975 0.9990 0.999519 0.6876 0.8610 1.0655 1.3277 1.7291 2.0930 2.5395 2.8609 3.1737 3.5794 3.883420 0.6870 0.8600 1.0640 1.3253 1.7247 2.0860 2.5280 2.8453 3.1534 3.5518 3.849521 0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.5176 2.8314 3.1352 3.5272 3.819322 0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.5083 2.8188 3.1188 3.5050 3.792123 0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.4999 2.8073 3.1040 3.4850 3.767624 0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.4922 2.7969 3.0905 3.4668 3.745425 0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.4851 2.7874 3.0782 3.4502 3.725126 0.6840 0.8557 1.0575 1.3150 1.7056 2.0555 2.4786 2.7787 3.0669 3.4350 3.706627 0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.4727 2.7707 3.0565 3.4210 3.689628 0.6834 0.8546 1.0560 1.3125 1.7011 2.0484 2.4671 2.7633 3.0469 3.4082 3.673929 0.6830 0.8542 1.0553 1.3114 1.6991 2.0452 2.4620 2.7564 3.0380 3.3962 3.659430 0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.4573 2.7500 3.0298 3.3852 3.646031 0.6825 0.8534 1.0541 1.3095 1.6955 2.0395 2.4528 2.7440 3.0221 3.3749 3.633532 0.6822 0.8530 1.0535 1.3086 1.6939 2.0369 2.4487 2.7385 3.0149 3.3653 3.621833 0.6820 0.8526 1.0530 1.3077 1.6924 2.0345 2.4448 2.7333 3.0082 3.3563 3.610934 0.6818 0.8523 1.0525 1.3070 1.6909 2.0322 2.4411 2.7284 3.0020 3.3479 3.600735 0.6816 0.8520 1.0520 1.3062 1.6896 2.0301 2.4377 2.7238 2.9960 3.3400 3.591136 0.6814 0.8517 1.0516 1.3055 1.6883 2.0281 2.4345 2.7195 2.9905 3.3326 3.582137 0.6812 0.8514 1.0512 1.3049 1.6871 2.0262 2.4314 2.7154 2.9852 3.3256 3.573738 0.6810 0.8512 1.0508 1.3042 1.6860 2.0244 2.4286 2.7116 2.9803 3.3190 3.565739 0.6808 0.8509 1.0504 1.3036 1.6849 2.0227 2.4258 2.7079 2.9756 3.3128 3.558140 0.6807 0.8507 1.0500 1.3031 1.6839 2.0211 2.4233 2.7045 2.9712 3.3069 3.551041 0.6805 0.8505 1.0497 1.3025 1.6829 2.0195 2.4208 2.7012 2.9670 3.3013 3.544242 0.6804 0.8503 1.0494 1.3020 1.6820 2.0181 2.4185 2.6981 2.9630 3.2960 3.537743 0.6802 0.8501 1.0491 1.3016 1.6811 2.0167 2.4163 2.6951 2.9592 3.2909 3.531644 0.6801 0.8499 1.0488 1.3011 1.6802 2.0154 2.4141 2.6923 2.9555 3.2861 3.525845 0.6800 0.8497 1.0485 1.3006 1.6794 2.0141 2.4121 2.6896 2.9521 3.2815 3.520346 0.6799 0.8495 1.0483 1.3002 1.6787 2.0129 2.4102 2.6870 2.9488 3.2771 3.515047 0.6797 0.8493 1.0480 1.2998 1.6779 2.0117 2.4083 2.6846 2.9456 3.2729 3.509948 0.6796 0.8492 1.0478 1.2994 1.6772 2.0106 2.4066 2.6822 2.9426 3.2689 3.505149 0.6795 0.8490 1.0475 1.2991 1.6766 2.0096 2.4049 2.6800 2.9397 3.2651 3.500450 0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.4033 2.6778 2.9370 3.2614 3.496051 0.6793 0.8487 1.0471 1.2984 1.6753 2.0076 2.4017 2.6757 2.9343 3.2579 3.491853 0.6791 0.8485 1.0467 1.2977 1.6741 2.0057 2.3988 2.6718 2.9293 3.2513 3.483854 0.6791 0.8483 1.0465 1.2974 1.6736 2.0049 2.3974 2.6700 2.9270 3.2481 3.480055 0.6790 0.8482 1.0463 1.2971 1.6730 2.0040 2.3961 2.6682 2.9247 3.2451 3.476456 0.6789 0.8481 1.0461 1.2969 1.6725 2.0032 2.3948 2.6665 2.9225 3.2423 3.472957 0.6788 0.8480 1.0459 1.2966 1.6720 2.0025 2.3936 2.6649 2.9204 3.2395 3.469658 0.6787 0.8479 1.0458 1.2963 1.6716 2.0017 2.3924 2.6633 2.9184 3.2368 3.466359 0.6787 0.8478 1.0456 1.2961 1.6711 2.0010 2.3912 2.6618 2.9164 3.2342 3.463260 0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.3901 2.6603 2.9146 3.2317 3.460261 0.6785 0.8476 1.0453 1.2956 1.6702 1.9996 2.3890 2.6589 2.9127 3.2293 3.457362 0.6785 0.8475 1.0452 1.2954 1.6698 1.9990 2.3880 2.6575 2.9110 3.2270 3.454563 0.6784 0.8474 1.0450 1.2951 1.6694 1.9983 2.3870 2.6561 2.9093 3.2247 3.451864 0.6783 0.8473 1.0449 1.2949 1.6690 1.9977 2.3860 2.6549 2.9076 3.2225 3.449165 0.6783 0.8472 1.0448 1.2947 1.6686 1.9971 2.3851 2.6536 2.9060 3.2204 3.446666 0.6782 0.8471 1.0446 1.2945 1.6683 1.9966 2.3842 2.6524 2.9045 3.2184 3.444167 0.6782 0.8470 1.0445 1.2943 1.6679 1.9960 2.3833 2.6512 2.9030 3.2164 3.441768 0.6781 0.8469 1.0444 1.2941 1.6676 1.9955 2.3824 2.6501 2.9015 3.2145 3.439469 0.6781 0.8469 1.0443 1.2939 1.6672 1.9949 2.3816 2.6490 2.9001 3.2126 3.437270 0.6780 0.8468 1.0442 1.2938 1.6669 1.9944 2.3808 2.6479 2.8987 3.2108 3.435071 0.6780 0.8467 1.0441 1.2936 1.6666 1.9939 2.3800 2.6469 2.8974 3.2090 3.432972 0.6779 0.8466 1.0440 1.2934 1.6663 1.9935 2.3793 2.6459 2.8961 3.2073 3.430873 0.6779 0.8466 1.0438 1.2933 1.6660 1.9930 2.3785 2.6449 2.8949 3.2057 3.428974 0.6778 0.8465 1.0437 1.2931 1.6657 1.9925 2.3778 2.6439 2.8936 3.2041 3.426975 0.6778 0.8464 1.0436 1.2929 1.6654 1.9921 2.3771 2.6430 2.8924 3.2025 3.425076 0.6777 0.8464 1.0436 1.2928 1.6652 1.9917 2.3764 2.6421 2.8913 3.2010 3.423277 0.6777 0.8463 1.0435 1.2926 1.6649 1.9913 2.3758 2.6412 2.8902 3.1995 3.421478 0.6776 0.8463 1.0434 1.2925 1.6646 1.9908 2.3751 2.6403 2.8891 3.1980 3.419779 0.6776 0.8462 1.0433 1.2924 1.6644 1.9905 2.3745 2.6395 2.8880 3.1966 3.418080 0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.3739 2.6387 2.8870 3.1953 3.416381 0.6775 0.8461 1.0431 1.2921 1.6639 1.9897 2.3733 2.6379 2.8860 3.1939 3.414782 0.6775 0.8460 1.0430 1.2920 1.6636 1.9893 2.3727 2.6371 2.8850 3.1926 3.413283 0.6775 0.8460 1.0429 1.2918 1.6634 1.9890 2.3721 2.6364 2.8840 3.1913 3.411684 0.6774 0.8459 1.0429 1.2917 1.6632 1.9886 2.3716 2.6356 2.8831 3.1901 3.410285 0.6774 0.8459 1.0428 1.2916 1.6630 1.9883 2.3710 2.6349 2.8822 3.1889 3.408787 0.6773 0.8458 1.0426 1.2914 1.6626 1.9876 2.3700 2.6335 2.8804 3.1866 3.405988 0.6773 0.8457 1.0426 1.2912 1.6624 1.9873 2.3695 2.6329 2.8795 3.1854 3.404589 0.6773 0.8457 1.0425 1.2911 1.6622 1.9870 2.3690 2.6322 2.8787 3.1843 3.403290 0.6772 0.8456 1.0424 1.2910 1.6620 1.9867 2.3685 2.6316 2.8779 3.1833 3.4019 100 0.6770 0.8452 1.0418 1.2901 1.6602 1.9840 2.3642 2.6259 2.8707 3.1737 3.3905 120 0.6765 0.8446 1.0409 1.2886 1.6577 1.9799 2.3578 2.6174 2.8599 3.1595 3.3735F分布19 2.99 2.61 2.40 2.27 2.18 2.06 2.02 1.98 1.86 1.81 1.7620 2.97 2.59 2.38 2.25 2.16 2.04 2.00 1.96 1.84 1.79 1.7421 2.96 2.57 2.36 2.23 2.14 2.02 1.98 1.95 1.83 1.78 1.7222 2.95 2.56 2.35 2.22 2.13 2.01 1.97 1.93 1.81 1.76 1.70 24 2.93 2.54 2.33 2.19 2.10 1.98 1.94 1.91 1.78 1.73 1.67 26 2.91 2.52 2.31 2.17 2.08 1.96 1.92 1.88 1.76 1.71 1.65 28 2.89 2.50 2.29 2.16 2.06 1.94 1.90 1.87 1.74 1.69 1.63 30 2.88 2.49 2.28 2.14 2.05 1.93 1.88 1.85 1.72 1.67 1.61P= 0.9911 9.65 7.21 6.22 5.67 5.32 4.89 4.74 4.63 4.40 4.29 4.21 4.15 4.1012 9.33 6.93 5.95 5.41 5.06 4.64 4.50 4.39 4.16 4.05 3.97 3.91 3.8613 9.07 6.70 5.74 5.21 4.86 4.44 4.30 4.19 3.96 3.86 3.78 3.72 3.6614 8.86 6.51 5.56 5.04 4.69 4.28 4.14 4.03 3.80 3.70 3.62 3.56 3.5115 8.68 6.36 5.42 4.89 4.56 4.14 4.00 3.89 3.67 3.56 3.49 3.42 3.3716 8.53 6.23 5.29 4.77 4.44 4.03 3.89 3.78 3.55 3.45 3.37 3.31 3.2617 8.40 6.11 5.18 4.67 4.34 3.93 3.79 3.68 3.46 3.35 3.27 3.21 3.1618 8.29 6.01 5.09 4.58 4.25 3.84 3.71 3.60 3.37 3.27 3.19 3.13 3.0819 8.18 5.93 5.01 4.50 4.17 3.77 3.63 3.52 3.30 3.19 3.12 3.05 3.0020 8.10 5.85 4.94 4.43 4.10 3.70 3.56 3.46 3.23 3.13 3.05 2.99 2.9421 8.02 5.78 4.87 4.37 4.04 3.64 3.51 3.40 3.17 3.07 2.99 2.93 2.8822 7.95 5.72 4.82 4.31 3.99 3.59 3.45 3.35 3.12 3.02 2.94 2.88 2.8323 7.88 5.66 4.76 4.26 3.94 3.54 3.41 3.30 3.07 2.97 2.89 2.83 2.7824 7.82 5.61 4.72 4.22 3.90 3.50 3.36 3.26 3.03 2.93 2.85 2.79 2.7425 7.77 5.57 4.68 4.18 3.85 3.46 3.32 3.22 2.99 2.89 2.81 2.75 2.7026 7.72 5.53 4.64 4.14 3.82 3.42 3.29 3.18 2.96 2.86 2.78 2.72 2.6628 7.64 5.45 4.57 4.07 3.75 3.36 3.23 3.12 2.90 2.79 2.72 2.65 2.6029 7.60 5.42 4.54 4.04 3.73 3.33 3.20 3.09 2.87 2.77 2.69 2.63 2.5730 7.56 5.39 4.51 4.02 3.70 3.30 3.17 3.07 2.84 2.74 2.66 2.60 2.55Excel公式1.正态分布函数Excel计算正态分布时，使用NORMDIST函数，其格式如下：NORMDIST（a，μ，σ，累积）其中，“累积”：若为TRUE，则输出分布函数值，即P{X≤a}；若为FALSE，则为概率密度函数值．示例：已知X服从正态分布，μ＝600，σ＝100，求P{X≤500}．输入公式NORMDIST(500, 600, 100, TRUE)得到的结果为0.158655，即P{X≤500}=0.158655．2、正态分布函数的反函数Excel计算正态分布函数的反函数使用NORMINV函数，格式如下：NORMINV（p，μ ，σ ），此公式计算a，使P{X ≤a}=p3标准正态分布反函数=NORMSINV(0.975)3、t分布Excel计算t分布的值,采用TDIST函数，格式如下：TDIST（a，自由度，侧数）其中，“侧数”：指明分布为单侧或双侧：若为1，为单侧；此命令输出P{ T >a }若为2，为双侧．此命令输出P{ |T| >a}示例：设T服从自由度为24的t分布，求P(T>1.711)．已知t＝1.711，df=24，采用单侧，则T分布的值：TDIST(1.711,24,1)得到0.05，即P(T > 1.711)=0.05．4. t分布的反函数Excel使用TINV函数得到t分布的反函数，格式如下：TINV（α，自由度）输出T 分布的α / 2 分位点：t_α/2_(n)若求临界值tα(n)，则使用公式＝TINV(2*α, n)5.返回F分布的函数是FDISTFDIST(x,degrees_freedom1,degrees_freedom2) 函数FDIST 的计算公式为FDIST=P( F>x )，5.F分布的反函数FINV(probability,deg_freedom1,deg_freedom2)已知probability=P( F>x )，求x。
概率统计分布表(常用)
25 10。
5197 11。
5240 13。
1197 14。
6114 16。
4734 19。
9393 29.3389 34.3816 37。
6525 40.6465 44.3141 46。
927926 11。
1602 12.1981 13。
8439 15。
3792 17.2919 20.8434 30。
4346 35.5632 38.8851 41。
9232 45。
6417 48.289927 11。
8076 12。
8785 14。
5734 16.1514 18.1139 21.7494 31.5284 36。
7412 40.1133 43.1945 46。
9629 49.644928 12.4613 13。
5647 15。
3079 16。
9279 18。
9392 22.6572 32。
6205 37。
9159 41。
3371 44.4608 48。
2782 50.993429 13.1211 14。
2565 16。
0471 17.7084 19.7677 23。
5666 33.7109 39.0875 42.5570 45.7223 49。
5879 52。
335630 13.7867 14。
9535 16。
7908 18。
4927 20。
5992 24.4776 34.7997 40。
2560 43。
7730 46。
9792 50。
8922 53。
672031 14。
4578 15。
6555 17。
5387 19.2806 21.4336 25。
3901 35.8871 41。
4217 44.9853 48.2319 52。
1914 55。
002732 15。
1340 16.3622 18。
2908 20。
0719 22。
2706 26.3041 36.9730 42。
5847 46.1943 49。
4804 53。
4858 56.328133 15.8153 17。
0735 19。
0467 20。
概率统计分布表(常用)
标准正态表标准文案标准文案标准文案标准文案T分布标准文案标准文案标准文案120 0.6765 0.8446 1.0409 1.2886 1.6577 1.9799 2.3578 2.6174 2.8599 3.1595 3.3735F分布P= 0.90标准文案P= 0.99标准文案标准文案标准文案标准文案标准文案标准文案标准文案标准文案标准文案Excel公式1.正态分布函数Excel计算正态分布时，使用NORMDIST函数，其格式如下：NORMDIST（a，μ，σ，累积）其中，“累积”：若为TRUE，则输出分布函数值，即P{X≤a}；若为FALSE，则为概率密度函数值．示例：已知X服从正态分布，μ＝600，σ＝100，求P{X≤500}．输入公式NORMDIST(500, 600, 100, TRUE)得到的结果为0.158655，即P{X≤500}=0.158655．2、正态分布函数的反函数Excel计算正态分布函数的反函数使用NORMINV函数，a}=p格式如下： NORMINV（p，μ，σ），此公式计算a，使P{X ≤3、 t分布Excel计算t分布的值,采用TDIST函数，其中，“侧数”：指明分布为单侧或双侧：若为1，为单侧；此命令输出P{ T >a }标准文案若为2，为双侧．此命令输出P{ |T| >a}示例：设T服从自由度为24的t分布，求P(T>1.711)．已知t＝1.711，df=24，采用单侧，则T分布的值：TDIST(1.711,24,1)得到0.05，即P(T > 1.711)=0.05．4. t分布的反函数Excel使用TINV函数得到t分布的反函数，格式如下： TINV（α，自由度）/2_(n)输出 T 分布的α / 2 分位点： t_αFDIST5.F分布的反函数已知 probability=P( F>x )，求x标准文案。
最常用的统计学概率分布总结含清晰图
1.随机变量分布函数 （1）累积分布函数(Cumulative Distribution Function (CDF)) If X is any random variable, then its CDF is defined for any real number x by
（2）CDF of F distribution
4
T= X Y /n
服从 df. 为 n 的 t-分布，记为 T ～ t(n)。 （1）PDF of t-distribution
（2）CDF of t-distribution
3
5. F-分布 X 和 Y 是相互独立的χ 分布随机变量，d.f 分别为 m 和 n，则称随机变量
F= X/m Y/n
服从 df.为 (m, n)的 F-分布，且通常写为 F～F（m,n）。 （1）PDF of F distribution
PX x
（2）概率密度函数(Probability Density Function (PDF)) The probability density function (PDF) f(x) of a continuous distribution iห้องสมุดไป่ตู้ defined as the derivative of the (cumulative) distribution function F(x),
d d
so we have
dt
2. 正态分布（normal distribution）
（1）概率密度函数（PDF）
以上结果可表示为 ~
|µ, σ ,.
1
µ
e
σ√2π
标准正态分布（standard normal distribution）表示为 N(0,1) xµ ~N 0,1 σ
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几种常见的概率分布表（内容源自书本，同时本人额外加了许多内容进去。
此表可直接打印）整理人：叶佩说明，我们学过的各种概率分布公式较多且形式多样，各分布的数学期望及方差是常用的数据，为方便做题目，也方便记忆故作此表，并在此共享给大家希望给大家提供一定方便！
类分布数学标记参数分布律或概率密度数学期望方差单点分布（退化
a a0
分布）
(0-1)分布（两点p1-p 分布或伯努利分
布）
二项分布
np np(1-p)
K=0,1,2⋯
负二项分布（帕
离斯卡分布）
散型
K=r,r+1,⋯
几何分布
K=1,2,⋯
超几何分布
N,M,n
(M ≤N,n≤
N)
泊松分布
K=0,1,2,⋯
均匀分布
其它正态分布（高斯
分布）
对数正态分布
若
且则 Y
服从该分布
逆高斯分布
其它
其它分布（伽玛分
连布）
其它
续型指数分布（负指
数分布）
注：指数分布是分布的特殊情况
其它
分布n2n
其它
非中心分布
其它
韦布尔分布
其它
拉普拉斯分布
瑞利分布
其它帕雷托分布
r,a>0
极值分布
注：若 X 服从韦布尔分布，则
逻辑斯蒂分布
分布
其它
柯西分布
t分布（学生氏
分布）
非中心 t 分布
F分布
其它非中心 F 分布
m,n 为二自
由度
其它
(r>1)(r>2)
( 是欧拉常数 )
服从分布。
不存在不存在
0 ，n>1
(n>1)
(n>2)
,
(n>2)
(n>4)。