概率统计分布表（常用）

标准正态表

x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.08 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 0.8106 0.8365 0.09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 1.0 0.8413 1.1 0.8643 1.2 0.8849 1.3 0.9032 1.4 0.9192 1.5 0.9332 1.6 0.9452 1.7 0.9554 1.8 0.9641 1.9 0.9713 2.0 0.9772 2.1 0.9821 2.2 0.9861 2.3 0.9893 2.4 0.9918 2.5 0.9938 2.6

0.9953

0.8438 0.8461 0.8665 0.8686 0.8869 0.8888 0.9049 0.9066 0.9207 0.9222 0.9345 0.9357 0.9463 0.9474 0.9564 0.9573 0.9649 0.9656 0.9719 0.9726 0.9778 0.9783 0.9826 0.9830 0.9864 0.9868 0.9896 0.9898 0.9920 0.9922 0.9940 0.9941 0.9955

0.9956

0.8485 0.8508 0.8708 0.8729 0.8907 0.8925 0.9082 0.9099 0.9236 0.9251 0.9370 0.9382 0.9484 0.9495 0.9582 0.9591 0.9664 0.9671 0.9732 0.9738 0.9788 0.9793 0.9834 0.9838 0.9871 0.9875 0.9901 0.9904 0.9925 0.9927 0.9943 0.9945 0.9957

0.9959

0.8531 0.8554 0.8749 0.8770 0.8944 0.8962 0.9115 0.9131 0.9265 0.9279 0.9394 0.9406 0.9505 0.9515 0.9599 0.9608 0.9678 0.9686 0.9744 0.9750 0.9798 0.9803 0.9842 0.9846 0.9878 0.9881 0.9906 0.9909 0.9929 0.9931 0.9946 0.9948 0.9960

0.9961

0.8577 0.8599 0.8790 0.8810 0.8980 0.8997 0.9147 0.9162 0.9292 0.9306 0.9418 0.9429 0.9525 0.9535 0.9616 0.9625 0.9693 0.9699 0.9756 0.9761 0.9808 0.9812 0.9850 0.9854 0.9884 0.9887 0.9911 0.9913 0.9932 0.9934 0.9949 0.9951 0.9962

0.9963

0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964

2.7 0.9965 2.8 0.9974 2.9 0.9981 3.0 0.9987 3.1 0.9990 3.2 0.9993 3.3 0.9995 3.4 0.9997 3.5 0.9998 3.6 0.9998 3.7 0.9999 3.8 0.9999 3.9

1.0000

0.9966 0.9967 0.9975 0.9976 0.9982 0.9982 0.9987 0.9987 0.9991 0.9991 0.9993 0.9994 0.9995 0.9995 0.9997 0.9997 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000

1.0000

0.9968 0.9969 0.9977 0.9977 0.9983 0.9984 0.9988 0.9988 0.9991 0.9992 0.9994 0.9994 0.9996 0.9996 0.9997 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000

1.0000

0.9970 0.9971 0.9978 0.9979 0.9984 0.9985 0.9989 0.9989 0.9992 0.9992 0.9994 0.9994 0.9996 0.9996 0.9997 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000

1.0000

0.9972 0.9973 0.9979 0.9980 0.9985 0.9986 0.9989 0.9990 0.9992 0.9993 0.9995 0.9995 0.9996 0.9996 0.9997 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.0000

1.0000

0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 1.0000

n\\p 1 2 3 4 5 6 7 8 9 10 11 0.005 0.0000 0.0100 0.0717 0.2070 0.4117 0.6757 0.9893 1.3444 1.7349 2.1559 2.6032 0.010 0.0002 0.0201 0.1148 0.2971 0.5543 0.8721 1.2390 1.6465 2.0879 2.5582 3.0535 0.025 0.0010 0.0506 0.2158 0.4844 0.8312 1.2373 1.6899 2.1797 2.7004 3.2470 3.8157 0.050 0.0039 0.1026 0.3518 0.7107 1.1455 1.6354 2.1673 2.7326 3.3251 3.9403 4.5748 0.100 0.0158 0.2107 0.5844 1.0636 1.6103 2.2041 2.8331 3.4895 4.1682 4.8652 5.5778 0.250 0.1015 0.5754 1.2125 1.9226 2.6746 3.4546 4.2549 5.0706 5.8988 6.7372 7.5841 0.750 1.3233 2.7726 4.1083 5.3853 6.6257 7.8408 9.0371 10.2189 11.3888 12.5489 13.7007 0.900 2.7055 4.6052 6.2514 7.7794 9.2364 10.6446 12.0170 13.3616 14.6837 15.9872 17.2750 0.950 3.8415 5.9915 7.8147 9.4877 11.0705 12.5916 14.0671 15.5073 16.9190 18.3070 19.6751 0.975 5.0239 7.3778 9.3484 11.1433 12.8325 14.4494 16.0128 17.5345 19.0228 20.4832 21.9200 0.990 6.6349 9.2103 11.3449 13.2767 15.0863 16.8119 18.4753 20.0902 21.6660 23.2093 24.7250 0.995 7.8794 10.5966 12.8382 14.8603 16.7496 18.5476 20.2777 21.9550 23.5894 25.1882 26.7568 12 3.0738 13 3.5650 14 4.0747 15 4.6009 16 5.1422 17 5.6972 18 6.2648 19 6.8440 20 7.4338 21 8.0337 22 8.6427 23 9.2604 24 9.8862 25 10.5197 26 11.1602 27 11.8076 28

12.4613 3.5706 4.1069 4.6604 5.2293 5.8122 6.4078 7.0149 7.6327 8.2604 8.8972 9.5425 4.4038 5.0088 5.6287 6.2621 6.9077 7.5642 8.2307 8.9065 9.5908 10.2829 10.9823 11.6886 12.4012 13.1197 13.8439 14.5734 15.3079 5.2260 5.8919 6.5706 7.2609 7.9616 8.6718 9.3905

6.3038 7.0415 7.7895 8.5468 9.3122 8.4384 9.2991 10.1653 11.0365 11.9122 12.7919 13.6753 14.5620 15.4518 16.3444 17.2396 18.1373 19.0373 19.9393 20.8434 21.7494 22.6572

14.8454 15.9839 17.1169 18.2451 19.3689 20.4887 21.6049 22.7178 23.8277 24.9348 26.0393 27.1413 28.2412 29.3389 30.4346 31.5284 32.6205

18.5493 19.8119 21.0641 22.3071 23.5418 24.7690 25.9894 27.2036 28.4120 29.6151 30.8133 32.0069 33.1962 34.3816 35.5632 36.7412 37.9159

21.0261 22.3620 23.6848 24.9958 26.2962 27.5871 28.8693 30.1435 31.4104 32.6706 33.9244 35.1725 36.4150 37.6525 38.8851 40.1133 41.3371

23.3367 24.7356 26.1189 27.4884 28.8454 30.1910 31.5264 32.8523 34.1696 35.4789 36.7807 38.0756 39.3641 40.6465 41.9232 43.1945 44.4608

26.2170 27.6882 29.1412 30.5779 31.9999 33.4087 34.8053 36.1909 37.5662 38.9322 40.2894 41.6384 42.9798 44.3141 45.6417 46.9629 48.2782

28.2995 29.8195 31.3193 32.8013 34.2672 35.7185 37.1565 38.5823 39.9968 41.4011 42.7957 44.1813 45.5585 46.9279 48.2899 49.6449 50.9934

10.1957 10.8564 11.5240 12.1981 12.8785 13.5647

10.1170 10.8508 11.5913 12.3380 13.0905 13.8484 14.6114 15.3792 16.1514 16.9279 10.0852 10.8649 11.6509 12.4426 13.2396 14.0415 14.8480 15.6587 16.4734 17.2919 18.1139 18.9392

29 13.1211 30 13.7867 31 14.4578 32 15.1340 33 15.8153 34 16.5013 35 17.1918 36 17.8867 37 18.5858 38 19.2889 39 19.9959 40 20.7065 41 21.4208 42 22.1385 43 22.8595 44 23.5837 45

24.3110

14.2565 14.9535 15.6555 16.3622 17.0735 17.7891 18.5089 19.2327 19.9602 20.6914 21.4262 22.1643 22.9056 23.6501 24.3976 25.1480 25.9013

16.0471 16.7908 17.5387 18.2908 19.0467 19.8063 20.5694 21.3359 22.1056 22.8785 23.6543 24.4330 25.2145 25.9987 26.7854 27.5746 28.3662

17.7084 18.4927 19.2806 20.0719 20.8665 21.6643 22.4650 23.2686 24.0749 24.8839 25.6954 26.5093 27.3256 28.1440 28.9647 29.7875 30.6123

19.7677 20.5992 21.4336 22.2706 23.1102 23.9523 24.7967 25.6433 26.4921 27.3430 28.1958 29.0505 29.9071 30.7654 31.6255 32.4871 33.3504

23.5666 24.4776 25.3901 26.3041 27.2194 28.1361 29.0540 29.9730 30.8933 31.8146 32.7369 33.6603 34.5846 35.5099 36.4361 37.3631 38.2910

33.7109 34.7997 35.8871 36.9730 38.0575 39.1408 40.2228 41.3036 42.3833 43.4619 44.5395 45.6160 46.6916 47.7663 48.8400 49.9129 50.9849

39.0875 40.2560 41.4217 42.5847 43.7452 44.9032 46.0588 47.2122 48.3634 49.5126 50.6598 51.8051 52.9485 54.0902 55.2302 56.3685 57.5053

42.5570 43.7730 44.9853 46.1943 47.3999 48.6024 49.8018 50.9985 52.1923 53.3835 54.5722 55.7585 56.9424 58.1240 59.3035 60.4809 61.6562

45.7223 46.9792 48.2319 49.4804 50.7251 51.9660 53.2033 54.4373 55.6680 56.8955 58.1201 59.3417 60.5606 61.7768 62.9904 64.2015 65.4102

49.5879 50.8922 52.1914 53.4858 54.7755 56.0609 57.3421 58.6192 59.8925 61.1621 62.4281 63.6907 64.9501 66.2062 67.4593 68.7095 69.9568

52.3356 53.6720 55.0027 56.3281 57.6484 58.9639 60.2748 61.5812 62.8833 64.1814 65.4756 66.7660 68.0527 69.3360 70.6159 71.8926 73.1661

T分布

n\\p 1 2 3 4 5 6 7 0.750 1.0000 0.8165 0.7649 0.7407 0.7267 0.7176 0.7111 0.800 1.3764 1.0607 0.9785 0.9410 0.9195 0.9057 0.8960 0.850 1.9626 1.3862 1.2498 1.1896 1.1558 1.1342 1.1192 0.900 3.0777 1.8856 1.6377 1.5332 1.4759 1.4398 1.4149 0.950 6.3138 2.9200 2.3534 2.1318 2.0150 1.9432 1.8946 0.975 12.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 0.990 31.8205 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 0.995 63.6567 9.9248 5.8409 4.6041 4.0321 3.7074 3.4995 0.9975 127.3213 14.0890 7.4533 5.5976 4.7733 4.3168 4.0293 0.9990 318.3088 22.3271 10.2145 7.1732 5.8934 5.2076 4.7853 0.9995 636.6192 31.5991 12.9240 8.6103 6.8688 5.9588 5.4079 8 0.7064 9 0.7027 10 0.6998 11 0.6974 12 0.6955 13 0.6938 14 0.6924 15 0.6912 16 0.6901 17 0.6892 18 0.6884 19 0.6876 20 0.6870 21 0.6864 22 0.6858 23 0.6853 24

0.6848

0.8889 1.1081 0.8834 1.0997 0.8791 1.0931 0.8755 1.0877 0.8726 1.0832 0.8702 1.0795 0.8681 1.0763 0.8662 1.0735 0.8647 1.0711 0.8633 1.0690 0.8620 1.0672 0.8610 1.0655 0.8600 1.0640 0.8591 1.0627 0.8583 1.0614 0.8575 1.0603 0.8569

1.0593

1.3968 1.8595 1.3830 1.8331 1.3722 1.8125 1.3634 1.7959 1.3562 1.7823 1.3502 1.7709 1.3450 1.7613 1.3406 1.7531 1.3368 1.7459 1.3334 1.7396 1.3304 1.7341 1.3277 1.7291 1.3253 1.7247 1.3232 1.7207 1.3212 1.7171 1.3195 1.7139 1.3178

1.7109

2.3060 2.8965 2.2622 2.8214 2.2281 2.7638 2.2010 2.7181 2.1788 2.6810 2.1604 2.6503 2.1448 2.6245 2.1314 2.6025 2.1199 2.5835 2.1098 2.5669 2.1009 2.5524 2.0930 2.5395 2.0860 2.5280 2.0796 2.5176 2.0739 2.5083 2.0687 2.4999 2.0639

2.4922

3.3554 3.8325 3.2498 3.6897 3.1693 3.5814 3.1058 3.4966 3.0545 3.4284 3.0123 3.3725 2.9768 3.3257 2.9467 3.2860 2.9208 3.2520 2.8982 3.2224 2.8784 3.1966 2.8609 3.1737 2.8453 3.1534 2.8314 3.1352 2.8188 3.1188 2.8073 3.1040 2.7969

3.0905

4.5008 5.0413 4.2968 4.7809 4.1437 4.5869 4.0247 4.4370 3.9296 4.3178 3.8520 4.2208 3.7874 4.1405 3.7328 4.0728 3.6862 4.0150 3.6458 3.9651 3.6105 3.9216 3.5794 3.8834 3.5518 3.8495 3.5272 3.8193 3.5050 3.7921 3.4850 3.7676 3.4668

3.7454

25 0.6844 26 0.6840 27 0.6837 28 0.6834 29 0.6830 30 0.6828 31 0.6825 32 0.6822 33 0.6820 34 0.6818 35 0.6816 36 0.6814 37 0.6812 38 0.6810 39 0.6808 40 0.6807 41

0.6805

0.8562 1.0584 0.8557 1.0575 0.8551 1.0567 0.8546 1.0560 0.8542 1.0553 0.8538 1.0547 0.8534 1.0541 0.8530 1.0535 0.8526 1.0530 0.8523 1.0525 0.8520 1.0520 0.8517 1.0516 0.8514 1.0512 0.8512 1.0508 0.8509 1.0504 0.8507 1.0500 0.8505

1.0497

1.3163 1.7081 1.3150 1.7056 1.3137 1.7033 1.3125 1.7011 1.3114 1.6991 1.3104 1.6973 1.3095 1.6955 1.3086 1.6939 1.3077 1.6924 1.3070 1.6909 1.3062 1.6896 1.3055 1.6883 1.3049 1.6871 1.3042 1.6860 1.3036 1.6849 1.3031 1.6839 1.3025

1.6829

2.0595 2.4851 2.0555 2.4786 2.0518 2.4727 2.0484 2.4671 2.0452 2.4620 2.0423 2.4573 2.0395 2.4528 2.0369 2.4487 2.0345 2.4448 2.0322 2.4411 2.0301 2.4377 2.0281 2.4345 2.0262 2.4314 2.0244 2.4286 2.0227 2.4258 2.0211 2.4233 2.0195

2.4208

2.7874 3.0782 2.7787 3.0669 2.7707 3.0565 2.7633 3.0469 2.7564 3.0380 2.7500 3.0298 2.7440 3.0221 2.7385 3.0149 2.7333 3.0082 2.7284 3.0020 2.7238 2.9960 2.7195 2.9905 2.7154 2.9852 2.7116 2.9803 2.7079 2.9756 2.7045 2.9712 2.7012

2.9670

3.4502 3.7251 3.4350 3.7066 3.4210 3.6896 3.4082 3.6739 3.3962 3.6594 3.3852 3.6460 3.3749 3.6335 3.3653 3.6218 3.3563 3.6109 3.3479 3.6007 3.3400 3.5911 3.3326 3.5821 3.3256 3.5737 3.3190 3.5657 3.3128 3.5581 3.3069 3.5510 3.3013

3.5442

42 0.6804 43 0.6802 44 0.6801 45 0.6800 46 0.6799 47 0.6797 48 0.6796 49 0.6795 50 0.6794 51 0.6793 52 0.6792 53 0.6791 54 0.6791 55 0.6790 56 0.6789 57 0.6788 58

0.6787

0.8503 1.0494 0.8501 1.0491 0.8499 1.0488 0.8497 1.0485 0.8495 1.0483 0.8493 1.0480 0.8492 1.0478 0.8490 1.0475 0.8489 1.0473 0.8487 1.0471 0.8486 1.0469 0.8485 1.0467 0.8483 1.0465 0.8482 1.0463 0.8481 1.0461 0.8480 1.0459 0.8479

1.0458

1.3020 1.6820 1.3016 1.6811 1.3011 1.6802 1.3006 1.6794 1.3002 1.6787 1.2998 1.6779 1.2994 1.6772 1.2991 1.6766 1.2987 1.6759 1.2984 1.6753 1.2980 1.6747 1.2977 1.6741 1.2974 1.6736 1.2971 1.6730 1.2969 1.6725 1.2966 1.6720 1.2963

1.6716

2.0181 2.4185 2.0167 2.4163 2.0154 2.4141 2.0141 2.4121 2.0129 2.4102 2.0117 2.4083 2.0106 2.4066 2.0096 2.4049 2.0086 2.4033 2.0076 2.4017 2.0066 2.4002 2.0057 2.3988 2.0049 2.3974 2.0040 2.3961 2.0032 2.3948 2.0025 2.3936 2.0017

2.3924

2.6981 2.9630 2.6951 2.9592 2.6923 2.9555 2.6896 2.9521 2.6870 2.9488 2.6846 2.9456 2.6822 2.9426 2.6800 2.9397 2.6778 2.9370 2.6757 2.9343 2.6737 2.9318 2.6718 2.9293 2.6700 2.9270 2.6682 2.9247 2.6665 2.9225 2.6649 2.9204 2.6633

2.9184

3.2960 3.5377 3.2909 3.5316 3.2861 3.5258 3.2815 3.5203 3.2771 3.5150 3.2729 3.5099 3.2689 3.5051 3.2651 3.5004 3.2614 3.4960 3.2579 3.4918 3.2545 3.4877 3.2513 3.4838 3.2481 3.4800 3.2451 3.4764 3.2423 3.4729 3.2395 3.4696 3.2368

3.4663

59 0.6787 60 0.6786 61 0.6785 62 0.6785 63 0.6784 64 0.6783 65 0.6783 66 0.6782 67 0.6782 68 0.6781 69 0.6781 70 0.6780 71 0.6780 72 0.6779 73 0.6779 74 0.6778 75

0.6778

0.8478 1.0456 0.8477 1.0455 0.8476 1.0453 0.8475 1.0452 0.8474 1.0450 0.8473 1.0449 0.8472 1.0448 0.8471 1.0446 0.8470 1.0445 0.8469 1.0444 0.8469 1.0443 0.8468 1.0442 0.8467 1.0441 0.8466 1.0440 0.8466 1.0438 0.8465 1.0437 0.8464

1.0436

1.2961 1.6711 1.2958 1.6706 1.2956 1.6702 1.2954 1.6698 1.2951 1.6694 1.2949 1.6690 1.2947 1.6686 1.2945 1.6683 1.2943 1.6679 1.2941 1.6676 1.2939 1.6672 1.2938 1.6669 1.2936 1.6666 1.2934 1.6663 1.2933 1.6660 1.2931 1.6657 1.2929

1.6654

2.0010 2.3912 2.0003 2.3901 1.9996 2.3890 1.9990 2.3880 1.9983 2.3870 1.9977 2.3860 1.9971 2.3851 1.9966 2.3842 1.9960 2.3833 1.9955 2.3824 1.9949 2.3816 1.9944 2.3808 1.9939 2.3800 1.9935 2.3793 1.9930 2.3785 1.9925 2.3778 1.9921

2.3771

2.6618 2.9164 2.6603 2.9146 2.6589 2.9127 2.6575 2.9110 2.6561 2.9093 2.6549 2.9076 2.6536 2.9060 2.6524 2.9045 2.6512 2.9030 2.6501 2.9015 2.6490 2.9001 2.6479 2.8987 2.6469 2.8974 2.6459 2.8961 2.6449 2.8949 2.6439 2.8936 2.6430

2.8924

3.2342 3.4632 3.2317 3.4602 3.2293 3.4573 3.2270 3.4545 3.2247 3.4518 3.2225 3.4491 3.2204 3.4466 3.2184 3.4441 3.2164 3.4417 3.2145 3.4394 3.2126 3.4372 3.2108 3.4350 3.2090 3.4329 3.2073 3.4308 3.2057 3.4289 3.2041 3.4269 3.2025

3.4250

76 0.6777 77 0.6777 78 0.6776 79 0.6776 80 0.6776 81 0.6775 82 0.6775 83 0.6775 84 0.6774 85 0.6774 86 0.6774 87 0.6773 88 0.6773 89 0.6773 90 0.6772 100 0.6770 120

0.6765

0.8464 1.0436 0.8463 1.0435 0.8463 1.0434 0.8462 1.0433 0.8461 1.0432 0.8461 1.0431 0.8460 1.0430 0.8460 1.0429 0.8459 1.0429 0.8459 1.0428 0.8458 1.0427 0.8458 1.0426 0.8457 1.0426 0.8457 1.0425 0.8456 1.0424 0.8452 1.0418 0.8446

1.0409

1.2928 1.6652 1.2926 1.6649 1.2925 1.6646 1.2924 1.6644 1.2922 1.6641 1.2921 1.6639 1.2920 1.6636 1.2918 1.6634 1.2917 1.6632 1.2916 1.6630 1.2915 1.6628 1.2914 1.6626 1.2912 1.6624 1.2911 1.6622 1.2910 1.6620 1.2901 1.6602 1.2886

1.6577

1.9917 2.3764 1.9913 2.3758 1.9908 2.3751 1.9905 2.3745 1.9901 2.3739 1.9897 2.3733 1.9893 2.3727 1.9890 2.3721 1.9886 2.3716 1.9883 2.3710 1.9879 2.3705 1.9876 2.3700 1.9873 2.3695 1.9870 2.3690 1.9867 2.3685 1.9840 2.3642 1.9799

2.3578

2.6421 2.8913 2.6412 2.8902 2.6403 2.8891 2.6395 2.8880 2.6387 2.8870 2.6379 2.8860 2.6371 2.8850 2.6364 2.8840 2.6356 2.8831 2.6349 2.8822 2.6342 2.8813 2.6335 2.8804 2.6329 2.8795 2.6322 2.8787 2.6316 2.8779 2.6259 2.8707 2.6174

2.8599

3.2010 3.4232 3.1995 3.4214 3.1980 3.4197 3.1966 3.4180 3.1953 3.4163 3.1939 3.4147 3.1926 3.4132 3.1913 3.4116 3.1901 3.4102 3.1889 3.4087 3.1877 3.4073 3.1866 3.4059 3.1854 3.4045 3.1843 3.4032 3.1833 3.4019 3.1737 3.3905 3.1595

3.3735

F分布

P=

n\\m 1 2 3 4 5 6 7 8 9 10 11 1 39.86 8.53 5.54 4.54 4.06 3.78 3.59 3.46 3.36 3.29 3.23 0.90

2 49.50 9.00 5.46 4.32 3.78 3.46 3.26 3.11 3.01 2.92 2.86 3 53.59 9.16 5.39 4.19 3.62 3.29 3.07 2.92 2.81 2.73 2.66 5 55.83 9.24 5.34 4.11 3.52 3.18 2.96 2.81 2.69 2.61 2.54

6 57.24 9.29 5.31 4.05 3.45 3.11 2.88 2.73 2.61 2.52 2.45 7 58.91 9.35 5.27 3.98 3.37 3.01 2.78 2.62 2.51 2.41 2.34 8 59.44 9.37 5.25 3.95 3.34 2.98 2.75 2.59 2.47 2.38 2.30 10 59.86 9.38 5.24 3.94 3.32 2.96 2.72 2.56 2.44 2.35 2.27 15 61.22 9.42 5.20 3.87 3.24 2.87 2.63 2.46 2.34 2.24 2.17 20 61.74 9.44 5.18 3.84 3.21 2.84 2.59 2.42 2.30 2.20 2.12 30 62.26 9.46 5.17 3.82 3.17 2.80 2.56 2.38 2.25 2.16 2.08 12 13 14 15 16 17 18 19 20 21 22 24 26 28 30

3.18 2.81 3.14 2.76 3.10 2.73 3.07 2.70 3.05 2.67 3.03 2.64 3.01 2.62 2.99 2.61 2.97 2.59 2.96 2.57 2.95 2.56 2.93 2.54 2.91 2.52 2.89 2.50 2.88

2.49

2.61 2.56 2.52 2.49 2.46 2.44 2.42 2.40 2.38 2.36 2.35 2.33 2.31 2.29 2.28

P= 2.48 2.39 2.43 2.35 2.39 2.31 2.36 2.27 2.33 2.24 2.31 2.22 2.29 2.20 2.27 2.18 2.25 2.16 2.23 2.14 2.22 2.13 2.19 2.10 2.17 2.08 2.16 2.06 2.14

2.05

0.99

2.28 2.24 2.23 2.20 2.19 2.15 2.16 2.12 2.13 2.09 2.10 2.06 2.08 2.04 2.06 2.02 2.04 2.00 2.02 1.98 2.01 1.97 1.98 1.94 1.96 1.92 1.94 1.90 1.93

1.88

2.21 2.10 2.16 2.05 2.12 2.01 2.09 1.97 2.06 1.94 2.03 1.91 2.00 1.89 1.98 1.86 1.96 1.84 1.95 1.83 1.93 1.81 1.91 1.78 1.88 1.76 1.87 1.74 1.85

1.72

2.06 2.01 2.01 1.96 1.96 1.91 1.92 1.87 1.89 1.84 1.86 1.81 1.84 1.78 1.81 1.76 1.79 1.74 1.78 1.72 1.76 1.70 1.73 1.67 1.71 1.65 1.69 1.63 1.67

1.61

n\\m 1 2 3 1 4052.18 98.50 34.12 2 3 5 6 7 8 10 12 14 16 18 20 4999.50 5403.35 5624.58 5763.65 5928.36 5981.07 6022.47 6106.32 6142.67 6170.10 6191.53 6208.73 99.00 30.82 99.17 29.46 99.25 28.71 99.30 28.24 99.36 27.67 99.37 27.49 99.39 27.35 99.42 27.05 99.43 26.92 99.44 26.83 99.44 26.75 99.45 26.69 4 5 6 7 8 9 10 11 12 13 14 15 16 21.20 18.00 16.26 13.27 13.75 10.92 12.25 9.55 11.26 8.65 10.56 8.02 10.04 7.56 9.65 7.21 9.33 6.93 9.07 6.70 8.86 6.51 8.68 6.36 8.53 6.23 15.98 11.39 9.78 9.15 8.45 7.85 7.59 7.01 6.99 6.42 6.55 5.99 6.22 5.67 5.95 5.41 5.74 5.21 5.56 5.04 5.42 4.89 5.29 4.77 15.52 14.98 10.97 10.46 8.75 8.26 7.46 6.99 6.63 6.18 6.06 5.61 5.64 5.20 5.32 4.89 5.06 4.64 4.86 4.44 4.69 4.28 4.56 4.14 4.44 4.03 14.80 14.66 10.29 10.16 8.10 7.98 6.84 6.72 6.03 5.91 5.47 5.35 5.06 4.94 4.74 4.63 4.50 4.39 4.30 4.19 4.14 4.03 4.00 3.89 3.89 3.78 14.25 9.89 9.77 7.72 7.60 6.47 6.36 5.67 5.56 5.11 5.01 4.71 4.60 4.40 4.29 4.16 4.05 3.96 3.86 3.80 3.70 3.67 3.56 3.55 3.45 14.08 9.68 9.61 7.52 7.45 6.28 6.21 5.48 5.41 4.92 4.86 4.52 4.46 4.21 4.15 3.97 3.91 3.78 3.72 3.62 3.56 3.49 3.42 3.37 3.31 9.55 7.40 6.16 5.36 4.81 4.41 4.10 3.86 3.66 3.51 3.37 3.26 16.69 12.06 14.37 14.15 14.02

17 18 19 20 21 22 23 24 25 26 27 28 29 30

8.40 6.11 8.29 6.01 8.18 5.93 8.10 5.85 8.02 5.78 7.95 5.72 7.88 5.66 7.82 5.61 7.77 5.57 7.72 5.53 7.68 5.49 7.64 5.45 7.60 5.42 7.56

5.39

5.18 4.67 5.09 4.58 5.01 4.50 4.94 4.43 4.87 4.37 4.82 4.31 4.76 4.26 4.72 4.22 4.68 4.18 4.64 4.14 4.60 4.11 4.57 4.07 4.54 4.04 4.51

4.02

4.34 3.93 4.25 3.84 4.17 3.77 4.10 3.70 4.04 3.64 3.99 3.59 3.94 3.54 3.90 3.50 3.85 3.46 3.82 3.42 3.78 3.39 3.75 3.36 3.73 3.33 3.70

3.30

3.79 3.68 3.71 3.60 3.63 3.52 3.56 3.46 3.51 3.40 3.45 3.35 3.41 3.30 3.36 3.26 3.32 3.22 3.29 3.18 3.26 3.15 3.23 3.12 3.20 3.09 3.17

3.07

3.46 3.35 3.37 3.27 3.30 3.19 3.23 3.13 3.17 3.07 3.12 3.02 3.07 2.97 3.03 2.93 2.99 2.89 2.96 2.86 2.93 2.82 2.90 2.79 2.87 2.77 2.84

2.74

3.27 3.21 3.19 3.13 3.12 3.05 3.05 2.99 2.99 2.93 2.94 2.88 2.89 2.83 2.85 2.79 2.81 2.75 2.78 2.72 2.75 2.68 2.72 2.65 2.69 2.63 2.66

2.60

3.16 3.08 3.00 2.94 2.88 2.83 2.78 2.74 2.70 2.66 2.63 2.60 2.57 2.55

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，

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FDIST FDIST(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

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