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。