Apéndice de Tablas

Manual y Prácticas de Estadística Administrativa I

Apéndice de Tablas

1. Números aleatorios

2. Distribución normal estandarizada acumulativa.

3. Valores críticos de t.

4. Probabilidades Binomiales.

5. Probabilidades de Poisson.

6. Factores de gráfica de control.

7. Distribución normal estandarizada.

Licenciatura en AdministraciónIng. Marco A. Parra R.

1


Tabla 1. - Números aleatorios

Fila0000112345

0000167890

1111112345

1111267890

2222212345

2222367890

3333312345

3333467890

01 49280 88924 35779 00283 81163 07275 89863 0234802 61870 41657 07468 08612 98083 97349 20775 4509103 43898 65923 25078 86129 78496 97653 91550 0807804 62993 93912 30454 84598 56095 20664 12872 6464705 33850 58555 51438 85507 71865 79488 76783 3170806 97340 03364 88472 04334 63919 36394 11095 9247007 70543 29776 10087 10072 55980 64688 68239 2046108 39382 93809 00796 95945 34101 81277 66090 8887209 37818 72142 67140 50785 22380 16703 53362 4494010 60430 22834 14130 96593 23298 56203 92671 1592511 82975 66158 84731 19436 55790 69229 28661 1367512 30987 71938 40355 54324 08401 26299 49420 5920813 55700 24586 93247 32596 11865 63397 44251 4318914 14756 23997 78643 75912 83832 32768 18928 5707015 32166 53251 70654 92827 63491 04233 33825 6966216 23236 75751 31888 81718 06546 83246 47651 0487717 45794 26926 15130 82455 78305 55058 52551 4718218 09893 20505 14225 68514 47427 56788 96297 7882219 54382 74598 91499 14523 68479 27686 46162 8355420 94750 89923 37089 20048 80336 94598 26940 3685821 70297 34135 53140 33340 42050 82341 44104 8294922 85157 47954 32979 26575 57600 40881 12250 7374223 11100 02340 12860 74697 96644 89439 28707 2581524 36871 50775 30592 57143 17381 68856 25853 3504125 23913 48357 63308 16090 51690 54607 72407 5553826 79348 36085 27973 65157 07456 22255 25626 5705427 92074 54641 53673 54421 18130 60103 69593 4946428 06873 21440 75593 41373 49502 17972 82578 1636429 12478 37622 99659 31065 83613 69889 58869 2957130 57175 55564 65411 42547 70457 03426 72937 8379231 91616 11075 80103 07831 59309 13276 26710 7300032 78025 75539 14621 39044 47450 03197 12787 4770933 27587 67228 80145 10175 12822 86687 65530 4932534 16690 20427 04251 64477 73709 73945 92396 6826335 70183 58065 65489 31833 82093 16747 10386 5929336 90730 35385 15679 99742 50866 78028 75573 6725737 10934 93242 13431 24590 02770 48585 00906 5859538 82462 30166 79613 47416 13389 80268 05085 9666639 27463 10433 07606 16285 93699 60912 94532 9563240 02979 52997 09079 92709 90110 47506 53693 4989241 46888 69929 75233 52507 32097 37594 10067 6732742 53638 83161 08289 12639 08141 12640 28437 0926843 82433 61427 17239 89160 19666 08814 37841 1284744 35766 31672 50082 22795 66948 65581 84393 1589045 10853 42581 08792 13257 61973 24450 52351 1660246 20341 27398 72906 63955 17276 10646 74692 4843847 54458 90542 77563 51839 52901 53355 83281 1917748 26337 66530 16687 35179 46560 00123 44546 7989649 34314 23729 85264 05575 96855 23820 11090 7982150 28603 10708 68933 34189 92166 15181 66628 58599

2


Tabla 2.- La distribución normal estandarizada acumulativa. Las entradas representan el área debajo de la curva normal desde hasta Z

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-3.9 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003-3.8 0.00007 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005-3.7 0.00011 0.00010 0.00010 0.00010 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008-3.6 0.00016 0.00015 0.00015 0.00014 0.00014 0.00013 0.00013 0.00012 0.00012 0.00011-3.5 0.00023 0.00022 0.00022 0.00021 0.00020 0.00019 0.00019 0.00018 0.00017 0.00017-3.4 0.00034 0.00032 0.00031 0.00030 0.00029 0.00028 0.00027 0.00026 0.00025 0.00024-3.3 0.00048 0.00047 0.00045 0.00043 0.00042 0.00040 0.00039 0.00038 0.00036 0.00035-3.2 0.00069 0.00066 0.00064 0.00062 0.00060 0.00058 0.00056 0.00054 0.00052 0.00050-3.1 0.00097 0.00094 0.00090 0.00087 0.00084 0.00082 0.00079 0.00076 0.00074 0.00071-3.0 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00111 0.00107 0.00103 0.00100-2.9 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 0.0099 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 0.059-1.4 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 0.2388 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 0.2482 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


3


Tabla 2.- La distribución normal estandarizada acumulativa. (continuación) Las entradas representan el área debajo de la curva normal desde hasta Z

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7518 0.75490.7 0.7580 0.7612 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 1.7881 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 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 1.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9383 0.9394 0.9406 0.9418 0.6429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 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 0.98172.1 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 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 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 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99897 0.999003.1 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.999293.2 0.99931 0.99934 0.99936 0.99938 0.99940 0.99942 0.99944 0.99946 0.99948 0.999503.3 0.99952 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.999653.4 0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99974 0.99975 0.999763.5 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.99982 0.99983 0.999833.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.999893.7 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992 0.99992 0.999923.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.999953.9 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997

Tabla 3.- Valores críticos de t.

4


Para un número particular de grados de libertad, la entrada representa el valor crítico de t correspondiente a un área de la cola superior específica ( ).

Grados de libertad 0.25 0.10 0.05 0.025 0.01 0.005

1 1.0000 3.0777 6.3138 12.7062 31.8207 63.65742 0.8165 1.8856 2.9200 4.3027 6.9646 9.92483 0.7649 1.6377 2.3534 3.1824 4.5407 5.84094 0.7407 1.5332 2.1318 2.7764 3.7469 4.60415 0.7267 1.4579 2.0150 2.5706 3.3649 4.03226 0.7176 1.4398 1.9432 2.4469 3.1427 3.70747 0.7111 1.4149 1.8946 2.3646 2.9980 3.49958 0.7064 1.3968 1.8595 2.3060 2.8965 3.35549 0.7027 1.3830 1.8331 2.2622 2.8214 3.249810 0.6998 1.3722 1.8125 2.2281 2.7638 3.1693

11 0.6974 1.3634 1.7959 2.2010 2.7181 3.105812 0.6955 1.3562 1.7823 2.1788 2.6810 3.054513 0.6938 1.3502 1.7709 2.1604 2.6503 3.012314 0.6924 1.3450 1.7613 2.1448 2.6245 2.976815 0.6912 1.3406 1.7531 2.1315 2.6025 2.946716 0.6901 1.3368 1.7459 2.1199 2.5835 2.920817 0.6892 1.3334 1.7396 2.1098 2.5669 2.898218 0.6884 1.3304 1.7341 2.1009 2.5524 2.878419 0.6876 1.3277 1.7291 2.0930 2.5395 2.860920 0.6870 1.3253 1.7247 2.0860 2.5280 2.8453

21 0.6864 1.3232 1.7207 2.0796 2.5177 2.831422 0.6858 1.3212 1.7171 2.0739 2.5083 2.818823 0.6853 1.3195 1.7139 2.0687 2.4999 2.807324 0.6848 1.3178 1.7109 2.0639 2.4922 2.796925 0.6844 1.3163 1.7081 2.0595 2.4851 2.787426 0.6840 1.3150 1.7056 2.0555 2.4786 2.778727 0.6837 1.3137 1.7033 2.0518 2.4727 2.770728 0.6834 1.3125 1.7011 2.0484 2.4671 2.763329 0.6830 1.3114 1.6991 2.0452 2.4620 2.756430 0.6828 1.3104 1.6973 2.0423 2.4573 2.7500

31 0.6825 1.3095 1.6955 2.0395 2.4528 2.744032 0.6822 1.3086 1.6939 2.0369 2.4487 2.738533 0.6820 1.3077 1.6924 2.0345 2.4448 2.733334 0.6818 1.3070 1.6909 2.0322 2.4411 2.728435 0.6816 1.3062 1.6896 2.0301 2.4377 2.723836 0.6814 1.3055 1.6883 2.0281 2.4345 2.719537 0.6812 1.3049 1.6871 2.0262 2.4314 2.715438 0.6810 1.3042 1.6860 2.0244 2.4286 2.711639 0.6808 1.3036 1.6849 2.0227 2.4258 2.707940 0.6807 1.3031 1.6839 2.0211 2.4233 2.7045

41 0.6805 1.3025 1.6829 2.0195 2.4208 2.701242 0.6804 1.3020 1.6820 2.0181 2.4185 2.698143 0.6802 1.3016 1.6811 2.0167 2.4163 2.695144 0.6801 1.3011 1.6802 2.0154 2.4141 2.692345 0.6800 1.3006 1.6794 2.0141 2.4121 2.689646 0.6799 1.3022 1.6787 2.0129 2.4102 2.687047 0.6797 1.2998 1.6779 2.0117 2.4083 2.684648 0.6796 1.2994 1.6772 2.0106 2.4066 2.6822

Tabla 3.- Valores críticos de t (continuación)


5

Áreas de la cola superior


Grados de libertad 0.25 0.10 0.05 0.025 0.01 0.005

49 0.6795 1.2991 1.6766 2.0096 2.4049 2.680050 0.6794 1.2987 1.6759 2.0086 2.4033 2.6778

51 0.6793 1.2984 1.6753 2.0076 2.4017 2.675752 0.6792 1.2980 1.6747 2.0066 2.4002 2.673753 0.6791 1.2977 1.6741 2.0057 2.3988 2.671854 0.6791 1.2974 1.6736 2.0049 2.3974 2.670055 0.6790 1.2971 1.6730 2.0040 2.3961 2.668256 0.6789 1.2969 1.6725 2.0032 2.3948 2.666557 0.6788 1.2966 1.6720 2.0035 2.3936 2.664958 0.6787 1.2963 1.6716 2.0017 2.3924 2.663359 0.6787 1.2961 1.6711 2.0010 2.3912 2.661860 0.6786 1.2958 1.6706 2.0003 2.3901 2.6603

61 0.6785 1.2956 1.6702 1.996 2.3890 2.658962 0.6785 1.2954 1.6698 1.9990 2.3880 2.657563 0.6784 1.2951 1.6694 1.9983 2.3870 2.656164 0.6783 1.2949 1.6690 1.9977 2.3860 2.654965 0.6783 1.2947 1.6686 1.9971 2.3851 2.653666 0.6782 1.2945 1.6683 1.9966 2.3842 2.652467 0.6782 1.2943 1.6679 1.9960 2.3833 2.651268 0.6781 1.2941 1.6676 1.9955 2.3824 2.650169 0.6781 1.2939 1.6672 1.9949 2.3816 2.649070 0.6780 1.2938 1.6669 1.9944 2.3808 2.6479

71 0.6780 1.2936 1.6666 1.9939 2.3800 2.646972 0.6779 1.2934 1.6663 1.9935 2.3793 2.645973 0.6779 1.2933 1.6660 1.9930 2.3785 2.644974 0.6778 1.2931 1.6657 1.9925 2.3778 2.643975 0.6778 1.2929 1.6654 1.9921 2.3771 2.643076 0.6777 1.2928 1.6652 1.9917 2.3764 2.642177 0.6777 1.2926 1.6649 1.9913 2.3758 2.641278 0.6776 1.2925 1.6646 1.9908 2.3751 2.640379 0.6776 1.2924 1.6644 1.9905 2.3745 2.639580 0.6776 1.2922 1.6641 1.9901 2.3739 2.6387

81 0.6775 1.2921 1.6639 1.9897 2.3733 2.637982 0.6775 1.2920 1.6636 1.9893 2.3727 2.637183 0.6775 1.2918 1.6634 1.9890 2.3721 2.636484 0.6774 1.2917 1.6632 1.9886 2.3717 2.635685 0.6774 1.2916 1.6630 1.9883 2.3710 2.634986 0.6774 1.2915 1.6628 1.9879 2.3705 2.634287 0.6773 1.2914 1.6626 1.9876 2.3700 2.633588 0.6773 1.2912 1.6624 1.9873 2.3695 2.632989 0.6773 1.2911 1.6622 1.9870 2.3690 2.632290 0.6772 1.2910 1.6620 1.9867 2.3685 2.6316

91 0.6772 1.2909 1.6618 1.9864 2.3680 2.630992 0.6772 1.2908 1.6616 1.9861 2.3676 2.630393 0.6771 1.2907 1.6614 1.9858 2.3671 2.629794 0.6771 1.2906 1.6612 1.9855 2.3667 2.629195 0.6771 1.2905 1.6611 1.9853 2.3662 2.628696 0.6771 1.2904 1.6609 1.9850 2.3658 2.628097 0.6770 1.2903 1.6607 1.9847 2.3654 2.627598 0.6770 1.2902 1.6606 1.9845 2.3650 2.626999 0.6770 1.2902 1.6604 1.9842 2.3646 2.6264100 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259

110 0.6767 1.2893 1.6588 1.9818 2.3607 2.6213

120 0.6765 1.2886 1.6577 1.9799 2.3578 2.6174

Tabla 4.- Probabilidades binomiales.

6

Áreas de la cola superior


n X .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .501 0 .9900 .9500 .9000 .8500 .8000 .7500 .7000 .6500 .6000 .5500 .5000

1 .0100 .0500 .1000 .1500 .2000 .2500 .3000 .3500 .4000 .4500 .50002 0 .9801 .9025 .8100 .7225 .6400 .5625 .4900 .4225 .3600 .3025 .2500

1 .0198 .0950 .1800 .2550 .3200 .3750 .4200 .4550 .4800 .4950 .50002 .0001 .0025 .0100 .0225 .0400 .0625 .0900 .1225 .1600 .2025 .25000

3 0 .9703 .8574 .7290 .6141 .5120 .4219 .3430 .2746 .2160 .1664 .12501 .0294 .1354 .2430 .3251 .3840 .4219 .4410 .4436 .4320 .4084 .37502 .0003 .0071 .0270 .0574 .0960 .1406 .1890 .2389 .2880 .3341 .37503 .0000 .0001 .0010 .0034 .0080 .0156 .0270 .0429 .0640 .0911 .1250

4 0 .9606 .8145 .6561 .5220 .4096 .3164 .2401 .1785 .1296 .0915 .06251 .0388 .1715 .2916 .3685 .4096 .4219 .4116 .3845 .3456 .2995 .25002 .0006 .0135 .0486 .0975 .1536 .2109 .2646 .3105 .3456 .3675 .37503 .0000 .0005 .0036 .0115 .0256 .0469 .0756 .1115 .1536 .2005 .25004 .0000 .0001 .0005 .0016 .0039 .0081 .0150 .0256 .0410 .0625

5 0 .9510 .7738 .5905 .4437 .3277 .2373 .1681 .1160 .0778 .0503 .03121 .0480 .2036 .3280 .3915 .4096 .3955 .3601 .3124 .2592 .2059 .15622 .0010 .0214 .0729 .1382 .2048 .2637 .3087 .3364 .3456 .3369 .31253 .0000 .0011 .0081 .0244 .0512 .0879 .1323 .1811 .2304 .2757 .31254 .0000 .0004 .0022 .0064 .0146 .0283 .0488 .0768 .1128 .15625 .0000 .0001 .0003 .0010 .0024 .0053 .0102 .0185 .0312

6 0 .9415 .7351 .5314 .3771 .2621 .1780 .1176 .0754 .0467 .0277 .01561 .0571 .2321 .3543 .3993 .3932 .3560 .3025 .2437 .1866 .1359 .09372 .0014 .0305 .0984 .1762 .2458 .2966 .3241 .3280 .3110 .2780 .23443 .0000 .0021 .0146 .0415 .0819 .1318 .1852 .2355 .2765 .3032 .31254 .0001 .0012 .055 .0154 .0330 .0595 .0951 .1372 .1681 .23445 .0000 .0001 .0004 .0015 .0044 .0102 .0205 .0369 .0609 .09376 .0000 .0000 .0001 .0002 .0007 .0018 .0041 .0083 .0156

7 0 .9321 .6983 .4783 .3206 .2097 .1335 .0824 .0490 .080 .0152 .00781 .0659 .2573 .3720 .3960 .3670 .3115 .2471 .1848 .1306 .0872 .05472 .0020 .0406 .1240 .2097 .2753 .3115 .3177 .2985 .2613 .2140 .16413 .0000 .0036 .0230 .0617 .1147 .1730 .2269 .2679 .2903 .2918 .27344 .0002 .0026 .0109 .0287 .0577 .0972 .1442 .1935 .2388 .27345 .0000 .0002 .0012 .0043 .0115 .0250 .0466 .0774 .1172 .16416 .0000 .0001 .0004 .0013 .0036 .0084 .0172 .0320 .05477 .0000 .0000 .0001 .0002 .0006 .0016 .0037 .0078

8 0 .9227 .6634 .4305 .2725 .1678 .1002 .0576 .0319 .0168 .0084 .00391 .0746 .2793 .3826 .3847 .3355 .2670 .1977 .1373 .0896 .0548 .03122 .0026 .0515 .1488 .2376 .2936 .3115 .2965 .2587 .2090 .1569 .10943 .0001 .0054 .0331 .0839 .1468 .2076 .2541 .2786 .2787 .2568 .21874 .0000 .0004 .0046 .0185 .0459 .0685 .1361 .1875 .2322 .2627 .27345 .0000 .0004 .0026 .0092 .0231 .0467 .0808 .1239 .1719 .21876 .0000 .0002 .0011 .0038 .0100 .0217 .0413 .0703 .10947 .0000 .0001 .0004 .0012 .0033 .0079 .0164 .03128 .0000 .0000 .0001 .0002 .0007 .0017 .0039

9 0 .9135 .6302 .3874 .2316 .1342 .0751 .0404 .0207 .0101 .0046 .00201 .0830 .2985 .3874 .3679 .3020 .2253 .1556 .1004 .0605 .0339 .01762 .0034 .0629 .1722 .2597 .3020 .3003 .2668 .2162 .1612 .1110 .07033 .0001 .0077 .0446 .1069 .1762 .2336 .2668 .2716 .2508 .2119 .16414 .0000 .0006 .0074 .0283 .0661 .1168 .1715 .2194 .2508 .2600 .24615 .0000 .0008 .0050 .0165 .0389 .0735 .1181 .1672 .2128 .24616 .0001 .0006 .0028 .0087 .0210 .0424 .0743 .1160 .16417 .0000 .0000 .0003 .0012 .0039 .0098 .0212 .0407 .07038 .0000 .0001 .0004 .0013 .0035 .0083 .01769 .0000 .0000 .0001 .0003 .0008 .0020

10 0 .9044 .5987 .3487 .1969 .1074 .0563 .0282 .0135 .0060 .0025 .00101 .0914 .3151 .3874 .3474 .2684 .1877 .1211 .0725 .0403 .0207 .00982 .0042 .0746 .1937 .2759 .3020 .2816 .2335 .1757 .1209 .0763 .04393 .0001 .0105 .0574 .1298 .2013 .2503 .2668 .2522 .2150 .1665 .11724 .0000 .0010 .0112 .0401 .0881 .1460 .2001 .2377 .2508 .2384 .20515 .0001 .0015 .0085 .0264 .0584 .1029 .1536 .2007 .2340 .2461

Tabla 4.- Probabilidades binomiales (continuación)


7


n X .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .5010 6 .0000 .0001 .0012 .0055 .0162 .0368 .0689 .1115 .1596 .2051

7 .0000 .0001 .0008 .0031 .0090 .0212 .0425 .0746 .11728 .0000 .0001 .0004 .0014 .0043 .0106 .0229 .04399 .0000 .0000 .0001 .0005 .0016 .0042 .009810 .0000 .0000 .0001 .0003 .0010

11 0 .8953 .5688 .3138 .1673 .0859 .0422 .0198 .0088 .0036 .0014 .00051 .0995 .3293 .3835 .3248 .2362 .1549 .0932 .0518 .0266 .0125 .00542 .0050 .0867 .2131 .2866 .2953 .2581 .1998 .1395 .0887 .0513 .02693 .0002 .0137 .0710 .1517 .2215 .2581 .2568 .2254 .1774 .1259 .08064 .0000 .0014 .0158 .0536 .1107 .1721 .2201 .3428 .2365 .2060 .16115 .0001 .0025 .0132 .0388 .0803 .1321 .1830 .2207 .2360 .22566 .0000 .0003 .0023 .0097 .0268 .0566 .0985 .1471 .1931 .22567 .0000 .0003 .0017 .0064 .0173 .0379 .0701 .1128 .16118 .0000 .0002 .0011 .0037 .0102 .0234 .0462 .08069 .0000 .0001 .0005 .0018 .0052 .0126 .026910 .0000 .000 .0002 .0007 .0021 .005411 .0000 .0000 .0002 .0005

12 0 .8864 .5404 .2824 .1422 .0687 .0317 .0138 .0057 .0022 .0008 .00021 .1074 .3413 .3766 .3012 .2062 .1267 .0712 .0368 .0174 .0075 .00292 .0060 .0988 .2301 .2924 .2835 .2323 .1678 .1088 .0639 .0339 .01613 .0002 .0173 .0852 .1720 .2362 .2581 .2397 .1954 .1419 .0923 .05374 .0000 .0021 .0213 .0683 .1329 .1936 .2311 .2367 .2128 .1700 .12085 .0002 .0038 .0193 .0532 .1032 .1585 .2039 .2270 .2225 .19346 .0000 .0005 .0040 .0155 .0401 .0792 .1281 .1766 .2124 .22567 .0000 .0006 .0033 .0115 .0291 .0591 .1009 .1489 .19348 .0001 .0005 .0024 .0078 .0199 .0420 .0762 .12089 .0000 .0001 .0004 .0015 .0048 .0125 .0277 .053710 .0000 .0000 .0002 .0008 .0025 .0068 .016111 .0000 .0001 .0003 .0010 .002912 .0000 .0000 .0001 .0002

13 0 .8775 .5133 .2542 .1209 .0550 .0238 .0097 .0037 .0013 .0004 .00011 .1152 .3512 .3672 .2774 .1787 .1029 .0540 .0259 .0113 .0045 .00162 .0070 .1109 .3448 .2937 .2680 .2059 .1388 .0836 .0453 .0220 .00953 .0003 .0214 .0997 .1900 .2457 .2517 .2181 .1651 .1107 .0660 .03494 .0000 .0028 .0277 .0838 .1535 .2097 .2337 .2222 .1845 .1350 .08735 .0003 .0055 .0266 .0691 .1258 .1803 .2154 .2314 .1989 .15716 .0000 .0008 .0063 .0230 .0559 .1030 .1546 .1968 .2169 .20957 .0001 .0011 .0058 .0186 .0442 .0833 .1312 .1775 .20958 .0001 .0001 .0011 .0047 .0142 .0336 .0656 .1089 .15719 .0000 .0000 .0001 .0009 .0034 .0101 .0243 .0495 .087310 .0000 .0001 .0006 .0022 .0065 .0162 .034911 .0000 .0001 .0003 .0012 .0036 .009512 .0000 .0000 .0001 .0005 .001613 .0000 .0000 .0001

14 0 .8687 .4877 .2288 .1028 .0440 .0178 .0068 .0024 .0008 .0002 .00011 .1229 .3593 .3559 .2539 .1539 .0832 .0407 .0181 .0073 .0027 .00092 .0081 .1229 .2570 .2912 .2501 .1802 .1134 .0634 .0317 .0141 .00563 .0003 .0259 .1142 .2056 .2501 .2402 .1943 .1366 .0845 .0462 .02224 .0000 .0037 .0349 .0998 .1720 .2202 .2290 .2022 .1549 .1040 .06115 .0004 .0078 .0352 .0860 .1468 .1963 .2178 .2066 .1701 .12226 .0000 .0013 .0093 .0322 .0734 .1262 .1759 .2066 .2068 .18337 .0002 .0019 .0092 .0280 .0618 .1082 .1574 .1952 .20958 .0000 .0003 .0020 .0082 .0232 .0510 .0918 .1398 .18339 .0000 .0003 .0018 .0066 .0183 .0408 .0762 .122210 .0000 .0003 .0014 .0049 .0136 .0312 .061111 .0000 .0002 .0010 .0033 .0093 .022212 .0000 .0001 .0005 .0019 .005613 .0000 .0001 .0002 .000914 .0000 .0000 .0001

15 0 .8601 .4633 .2059 .0874 .0352 .0134 .0047 .0016 .0005 .0001 .00001 .1303 .3658 .3432 .2312 .1319 .0668 .0305 .0126 .0047 .0016 .0005

8


Tabla 4.- Probabilidades binomiales (continuación)n X .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .5015 2 .0092 .1348 .2059 .2856 .2309 .1559 .0916 .0476 .0219 .0090 .0032

3 .0004 .0307 .3432 .2184 .2501 .2252 .1700 .1110 .0634 .0318 .01394 .0000 .0049 .2669 .1156 .1876 .2252 .2186 .1792 .1268 .0780 .04175 .0006 .1285 .0449 .1032 .1651 .2061 .2123 .1839 .1404 .09166 .0000 .0428 .0132 .0430 .0917 .1472 .1906 .2066 .1914 .15277 .0105 .0030 .0138 .0393 .0811 .1319 .1771 .2013 .19648 .0019 .0005 .0035 .0131 .0348 .0710 .1181 .1647 .19649 .0003 .0001 .0007 .0034 .0116 .0298 .0612 .1048 .152710 .0000 .0000 .0001 .0007 .0030 .0096 .0245 .0515 .091611 .0000 .0001 .0006 .0024 .0074 .0191 .041712 .0000 .0001 .0004 .0016 .0052 .013913 .0000 .0001 .0003 .0010 .003214 .0000 .0000 .0001 .000515 .0000 .0000

16 0 .8515 .4401 .1853 .0743 .0281 .0100 .0033 .0010 .0003 .0001 .00001 .1376 .3706 .3294 .2097 .1126 .0535 .0228 .0087 .0030 .0009 .00022 .0104 .1463 .2745 .2775 .211 .1336 .0732 .0353 .0150 .0056 .00183 .0005 .0359 .1423 .2285 .2463 .2079 .165 .0888 .0468 .0215 .00854 .0000 .0061 .0514 .1311 .2001 .2252 .2040 .1553 .1014 .0572 .02785 .0008 .0137 .0555 .1201 .1802 .2099 .2008 .1623 .1123 .06676 .0001 .0028 .0180 .0550 .1101 .1649 .1982 .1983 .1684 .12227 .0000 .0004 .0045 .0197 .0524 .1010 .1524 .1889 .1969 .17468 .0001 .0009 .0055 .0197 .0487 .0923 .1417 .1812 .19649 .0000 .0001 .0012 .0058 .0185 .0442 .0840 .1318 .174610 .0000 .0002 .0014 .0056 .0167 .0392 .0755 .122211 .0000 .0002 .0013 .0049 .0142 .0337 .066712 .0000 .0002 .0011 .0040 .0115 .027813 .0000 .0002 .0008 .0029 .008514 .0000 .0001 .0005 .001815 .0000 .0001 .000216 .0000 .0000

17 0 .8429 .4181 .1668 .0631 .0225 .0075 .0023 .0007 .0002 .0000 .00001 .1447 .3741 .3150 .1893 .0957 .0426 .0169 .0060 .0019 .0005 .00012 .0117 .1575 .2800 .2673 .1914 .1136 .0581 .0260 .0102 .0035 .00103 .0006 .0415 .1556 .2359 .2393 .1893 .1245 .0701 .0341 .0144 .00524 .0000 .0076 .0605 .1457 .2093 .2209 .1868 .1320 .0796 .0411 .01825 .0010 .0175 .0668 .1361 .1914 .2081 .1849 .1379 .0875 .04726 .0001 .0039 .0236 .0680 .1276 .1784 .1991 .1839 .1412 .09447 .0000 .0007 .0065 .0267 .0668 .1201 .1685 .1927 .1841 .14848 .0001 .0014 .0084 .0279 .0644 .1134 .1606 .1883 .18559 .0000 .0003 .0021 .0093 .0276 .0611 .1070 .1540 .185510 .0000 .0004 .0025 .0095 .0263 .0571 .1008 .148411 .0001 .0005 .0026 .0090 .0242 .0525 .094412 .0000 .0001 .0006 .0024 .0081 .0215 .047213 .0000 .0001 .0005 .0021 .0068 .018214 .0000 .0001 .0004 .0016 .005215 .0000 .0001 .0003 .001016 .0000 .0000 .000117 .0000

18 0 .8345 .3972 .1501 .0536 .0180 .0056 .0016 .0004 .0001 .0000 .00001 .1517 .3763 .3002 .1704 .0811 .0338 .0126 .0042 .0012 .0003 .00012 .0130 .1683 .2835 .2556 .1723 .0958 .0458 .0190 .0069 .0022 .00063 .0007 .0473 .1680 .2406 .2297 .1704 .1046 .0547 .0246 .0095 .00314 .0000 .0093 .0700 .1592 .2153 .2130 .1681 .1104 .0614 .0291 .01175 .0014 .0218 .0787 .1507 .1988 .2017 .1664 .1146 .0666 .03276 .0002 .0052 .0301 .0816 .1436 .1873 .1941 .1655 .1181 .07087 .0000 .0010 .0091 .0350 .0820 .1376 .1792 .1892 .1657 .12148 .0002 .0022 .0120 .0376 .0811 .1327 .1734 .1864 .16699 .0000 .0004 .0033 .0139 .0386 .0794 .1284 .1694 .185510 .0001 .0008 .0042 .0149 .0385 .0771 .1248 .1669



9


n X .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50

10


18 11 .0000 .0001 .0010 .0046 .0151 .0374 .0742 .121412 .0000 .0002 .0012 .0047 .0145 .0354 .0708

13 .0000 .0002 .0012 .0045 .0134 .032714 .0000 .0002 .0011 .0039 .011715 .0000 .0002 .0009 .003116 .0000 .0001 .000617 .0000 .000118 .0000

19 0 .8262 .3774 .1351 .0456 .0144 .0042 .0011 .0003 .0001 .0000 .00001 .1586 .3774 .2852 .1529 .0685 .0268 .0093 .0029 .0008 .0002 .00002 .0144 .1787 .2852 .2428 .1540 .0803 .0358 .0138 .0046 .0013 .00033 .0008 .0533 .196 .2428 .2182 .1517 .0869 .0422 .0175 .0062 .00184 .0000 .0112 .0798 .1714 .1636 .2023 .1491 .0909 .0467 .0203 .00745 .0018 .0266 .0907 .0955 .2023 .1916 .1468 .0933 .0497 .02226 .0002 .0069 .0374 .0443 .1574 .1916 .1844 .1451 .0949 .05187 .0000 .0014 .0122 .0166 .0974 .1525 .1489 .1797 .1443 .09618 .0002 .0032 .0051 .0487 .0981 .0980 .1797 .1771 .14429 .0000 .0007 .0013 .0198 .0514 .0528 .1464 .1771 .176210 .0001 .0003 .0066 .0220 .0233 .0976 .1449 .176211 .0000 .0000 .0018 .077 .0083 .0532 .0970 .144212 .0004 .0022 .0024 .0237 .0529 .096113 .0001 .0005 .0006 .0085 .0233 .051814 .0000 .0001 .0001 .0024 .0082 .022215 .0000 .0000 .0005 .0022 .007416 .0001 .0005 .001817 .0000 .0001 .000318 .0000 .000019 .0000

20 0 .8179 .3585 .1216 .0388 .0115 .0032 .0008 .0002 .0000 .0000 .00001 .1652 .3774 .2702 .1368 .0576 .0211 .0068 .0020 .0005 .0001 .00002 .0159 .1887 .2852 .2293 .1369 .0669 .0278 .0100 .0031 .0008 .00023 .0010 .0596 .1901 .3428 .2054 .1339 .0716 .0323 .0123 .0040 .00114 .0000 .0133 .0898 .1821 .2182 .1897 .1304 .0738 .0350 .0139 .00465 .0022 .0319 .1028 .1746 .2023 .1789 .1272 .0746 .0365 .01486 .0003 .0089 .0454 .1091 .1686 .1916 .1712 .1244 .0746 .03707 .0000 .0020 .0160 .0545 .1124 .1643 .1844 .1659 .1221 .07398 .0004 .0046 .0222 .0609 .1144 .1614 .1797 .1623 .12019 .0001 .0011 .0074 .0271 .0654 .1158 .1597 .1771 .160210 .0000 .0002 .0020 .0099 .0308 .0686 .1171 .1593 .176211 .0000 .0005 .0030 .0120 .0336 .0710 .1185 .160212 .0001 .0008 .0039 .0136 .0355 .0727 .120113 .0000 .0002 .0010 .0045 .0146 .0366 .073914 .0000 .0002 .0012 .0049 .0150 .037015 .0000 .0003 .0013 .0049 .014816 .0000 .0003 .0013 .004617 .0000 .0002 .001118 .0000 .000219 .000020 .0000

25 0 .7778 .2774 .0718 .0172 .0038 .0008 .0001 .0000 .0000 .0000 .00001 .1964 .3650 .1994 .0759 .0236 .0063 .0014 .0003 .0000 .0000 .00002 .0238 .2305 .2659 .1607 .0708 .0251 .0074 .0018 .0004 .0001 .00003 .0018 .0930 .2265 .2174 .1358 .0641 .0343 .0076 .0019 .0004 .00014 .0001 .0269 .1384 .2110 .1867 .1175 .0572 .0234 .0071 .0018 .00045 .0000 .0060 .0646 .1564 .1960 .1645 .1030 .0506 .0199 .0063 .00166 .0010 .0239 .0920 .1633 .1828 .1472 .0908 .0442 .0172 .00537 .0001 .0072 .0441 .1108 .1654 .1712 .1327 .0800 .0381 .01438 .0000 .0018 .0175 .0623 .1241 .1651 .1607 .1200 .0701 .03229 .0004 .0058 .0294 .0781 .1336 .1615 .1511 .1084 .060910 .0000 .0016 .0118 .0417 .0916 .1409 .1612 .1419 .0974



11


Tabla 5.- Probabilidades de Poisson.

n X .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .5025 11 .0004 .0040 .0189 .0536 .1034 .1465 .1583 .1328

12 .0000 .0012 .0074 .0268 .0650 .1140 .1511 .155013 .0003 .0025 .0115 .0350 .0760 .1236 .155014 .0000 .0007 .0042 .0161 .0434 .0867 .132815 .0002 .0013 .0064 .0212 .0520 .097416 .0000 .0004 .0021 .0088 .0266 .060917 .0001 .0006 .0031 .0115 .032218 .0000 .0001 .0009 .0042 .014319 .0000 .0002 .0013 .005320 .0000 .0001 .001621 .0000 .000422 .000123 .0000

30 0 .7397 .2146 .0424 .0076 .0012 .0002 .0000 .0000 .0000 .0000 .00001 .2242 .3389 .1413 .0404 .0093 .0018 .0003 .0000 .0000 .0000 .00002 .0328 .2586 .2277 .1034 .0337 .0086 .0018 .0003 .0000 .0000 .00003 .0031 .1270 .2361 .1703 .0785 .0269 .0072 .0015 .0003 .0000 .00004 .0002 .0451 .1771 .2028 .1325 .0604 .0208 .0056 .0012 .0002 .00005 .0000 .0124 .1023 .1861 .1723 .1047 .0464 .0157 .0041 .0008 .00016 .0027 .0474 .1368 .1795 .1455 .0829 .0353 .0115 .0029 .00067 .0005 .0180 .0828 .1538 .1662 .1219 .0652 .0263 .0081 .00198 .0001 .0058 .0420 .1106 .1593 .1501 .1009 .0505 .0191 .00559 .0000 .0016 .0181 .0676 .1298 .1573 .1328 .0823 .0382 .013310 .0004 .0067 .0355 .0909 .1416 .1502 .1152 .0656 .028011 .0001 .0022 .0161 .0551 .1103 .1471 .1396 .0976 .050912 .0000 .0006 .0064 .0291 .0749 .1254 .1474 .1265 .080613 .0001 .0022 .0134 .0444 .0935 .1360 .1433 .111514 .0000 .0007 .0054 .0231 .0611 .1101 .1424 .135415 .0002 .0019 .0106 .0351 .0783 .1242 .144516 .0000 .0006 .0042 .0177 .0489 .0953 .135417 .0002 .0015 .0079 .0269 .0642 .111518 .0000 .0005 .0031 .0129 .0379 .080619 .0001 .0010 .0054 .0196 .050920 .0000 .0003 .0020 .0088 .028021 .0001 .0006 .0034 .013322 .0000 .0002 .0012 .005523 .0000 .0003 .001924 .0001 .000625 .0000 .0001

12



X 0.1 0.2 0.3 .04 λ0.5 0.6 0.7 0.8 0.9 1.0

0 .9048 .8187 .7408 .6703 .6065 .5488 .4966 .4493 .4066 .36791 .0905 .1637 .2222 .2681 .3033 .3293 .3476 .3595 .3569 .36792 .0045 .0164 .0333 .0536 .0758 .0988 .1217 .1438 .1647 .18393 .0002 .0011 .0033 .0072 .0126 .0198 .0284 .0383 .0494 .06134 .0000 .0001 .0002 .0007 .0016 .0030 .0050 .0077 .0111 .01535 .0000 .0000 .0001 .0002 .0004 .0007 .0012 .0020 .00316 .0000 .0000 .0000 .0001 .0002 .0003 .00057 .0000 .0000 .0000 .0001

X 1.1 1.2 1.3 1.4 λ1.5 1.6 1.7 1.8 1.9 2.0

0 .3329 .3012 .2725 .2466 .2231 .2019 .1827 .1653 .1496 .13531 .3662 .3614 .3543 .3452 .3347 .3230 .3106 .2975 .2842 .27072 .2014 .2169 .2503 .2417 .2510 .2584 .2640 .2678 .2700 .27073 .0738 .0867 .0998 .1128 .1255 .1378 .1496 .1607 .1710 .18044 .02.3 .0260 .0324 .0395 .0471 .0551 .0636 .0723 .0812 .09025 .0045 .0062 .0084 .0111 .0141 .0176 .0216 .0260 .0309 .03616 .0008 .0012 .0018 .0026 .0035 .0047 .0061 .0078 .0098 .01207 .0001 .0002 .0003 .0005 .0008 .0011 .0015 .0020 .0027 .00348 .0000 .0000 .0001 .0001 .0001 .0002 .0003 .0005 .0006 .00099 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0002

X 2.1 2.2 2.3 2.4 λ2.5 2.6 2.7 2.8 2.9 3.0

0 .1225 .1108 .1003 .0907 .0821 .0743 .0672 .0608 .0550 .04981 .2572 .2438 .2306 .2177 .2052 .1931 .1815 .1703 .1396 .14942 .2700 .2681 .2652 .2613 .2565 .2510 .2450 .2384 .2314 .22403 .1890 .1966 .2033 .2090 .2138 .2176 .2205 .2225 .2237 .22404 .0992 .1082 .1169 .1254 .1336 .1414 .1488 .1557 .1622 .16805 .0417 .0476 .0538 .0602 .0668 .0735 .0804 .0872 .0940 .10086 .0146 .0174 .0206 .0241 .0278 .0319 .0362 .0407 .0455 .05047 .0044 .0055 .0068 .0083 .0099 .0118 .0139 .0163 .0188 .02168 .0011 .0015 .0019 .0025 .0031 .0038 .0047 .0057 .0068 .00819 .0003 .0004 .0005 .0007 .0009 .0011 .0014 .0018 .0022 .0027

10 .0001 .0001 .0001 .0002 .0002 .0003 .0004 .0005 .0006 .000811 .0000 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0002 .000212 .0000 .0000 .0000 .0000 .0001

X 3.1 3.2 3.3 3.4 λ3.5 3.6 3.7 3.8 3.9 4.0

0 .0450 .0408 .0369 .0334 .0302 .0273 .0247 .0224 .0202 .01831 .1397 .1304 .1217 .1135 .1057 .0984 .0915 .0850 .0789 .07332 .2165 .2087 .2008 .1929 .1850 .1771 .1692 .1615 .1539 .14653 .2237 .2226 .2209 .2186 .2158 .2125 .2087 .2046 .2001 .19544 .1734 .1781 .1823 .1858 .1888 .1912 .1931 .1944 .1951 .19545 .1075 .1140 .1203 .1264 .1322 .1377 .1429 .1477 .1522 .15636 .0555 .0608 .0662 .0716 .0771 .026 .0881 .0936 .0989 .10427 .0246 .0278 .0312 .0348 .0385 .0425 .0466 .0508 .0551 .05958 .0095 .0111 .0129 .0148 .0169 .0191 .0215 .0241 .0269 .02989 .0033 .0040 .0047 .0056 .0066 .0076 .0089 .0102 .0116 .0132

10 .0010 .0013 .0016 .0019 .0023 .0028 .0033 .0039 .0045 .005311 .0003 .0004 .0005 .0006 .0007 .0009 .0011 .0013 .0016 .001912 .0001 .0001 .0001 .0002 .0002 .0003 .0003 .0004 .0005 .000613 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0001 .0002 .000214 .0000 .0000 .0000 .0000 .0000 .0001

13


Tabla 5.- Probabilidades de Poisson. (Continuación)

X 4.1 4.2 4.3 4.4 λ4.5 4.6 4.7 4.8 4.9 5.0

0 .0166 .0150 .0136 .0123 .0111 .0101 .0091 .0082 .0074 .00671 .0679 .0630 .0583 .0540 .0500 .0462 .0427 .0395 .0365 .03372 .1393 .1323 .1254 .1158 .1125 .1063 .1005 .0948 .0894 .08423 .1904 .1852 .1798 .1743 .1687 .1631 .1574 .1517 .1460 .14044 .1951 .1944 .1933 .1917 .1898 .1875 .1849 .1820 .1789 .17555 .1600 .1633 .1662 .1687 .1708 .1725 .1738 .1747 .1753 .17556 .1093 .1143 .1191 .1237 .1281 .1323 .1362 .1398 .1432 .14627 .0640 .0686 .0732 .0778 .0824 .0869 .0914 .0959 .1002 .10448 .0328 .0360 .0393 .0428 .0463 .0500 .0537 .0575 .0614 .06539 .0150 .0168 .0188 .0209 .0232 .0255 .0280 .0307 .0334 .0363

10 .0061 .0071 .0081 .0092 .0104 .0118 .0132 .0147 .0164 .018111 .0023 .0027 .0032 .0037 .0043 .0049 .0056 .0064 .0073 .008212 .0008 .0009 .0011 .0014 .0016 .0019 .0022 .0026 .0030 .003413 .0002 .0003 .0004 .0005 .0006 .0007 .0008 .0009 .0011 .001314 .0001 .0001 .0001 .0001 .0002 .0002 .0003 .0003 .0004 .000515 .0000 .0000 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0002

X 5.1 5.2 5.3 5.4 λ

5.5 5.6 5.7 5.8 5.9 6.00 .0061 .0055 .0050 .0045 .0041 .0037 .0037 .0030 .0027 .00251 .0311 .0287 .0265 .0244 .0255 .0207 .0191 .0176 .0162 .01492 .0793 .0746 .0701 .0659 .0618 .0580 .0544 .0509 .0477 .04463 .1348 .1293 .1239 .1185 .1133 .1082 .1033 .0985 .0938 .08924 .1719 .1681 .1641 .1600 .1558 .1515 .1472 .1428 .1383 .13395 .1753 .1748 .1740 .1728 .1714 .1697 .1678 .1656 .1632 .16066 .1490 .1515 .1537 .1555 .1571 .1584 .1594 .1601 .1605 .16067 .1086 .1125 .1163 .1200 .1234 .1267 .1298 .1326 .1353 .13778 .0692 .0731 .0771 .0810 .0849 .0887 .0925 .0962 .0998 .10339 .0392 .0423 .0454 .0486 .0519 .0552 .0586 .0620 .0654 .0688

10 .0200 .0220 .0241 .0262 .0285 .0309 .0334 .0359 .0386 .041311 .0093 .0104 .0116 .0129 .0143 .0157 .0173 .0190 .0207 .022512 .0039 .0045 .0051 .0058 .0065 .0073 .0082 .0092 .0102 .011313 .0015 .0018 .0021 .0024 .0028 .0032 .0036 .0041 .0046 .005314 .0006 .0007 .0008 .0009 .0011 .0013 .0015 .0017 .0019 .002215 .0002 .0002 .0003 .0003 .0004 .0005 .0006 .0007 .0008 .000916 .0001 .0001 .0001 .0001 .0001 .0002 .0002 .0002 .0003 .000317 .0000 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0001 .0001

X 6.1 6.2 6.3 6.4 λ

6.5 6.6 6.7 6.8 6.9 7.00 .0022 .0020 .0018 .0017 .0015 .0014 .0012 .0011 .0010 .00091 .0137 .0126 .0116 .0106 .0098 .0090 .0082 .0076 .0070 .00642 .0417 .0390 .0364 .0340 .0318 .0296 .0276 .0258 .0240 .02233 .0848 .0806 .0765 .0726 .0688 .0652 .0617 .0584 .0552 .05214 .1294 .1249 .1205 .1162 .1118 .1076 .1034 .0992 .0952 .09125 .1579 .1549 .1519 .1487 .1454 .1420 .1385 .1349 .1314 .12776 .1605 .1601 .1595 .1586 .1575 .1562 .1546 .1529 .1511 .14907 .1399 .1418 .1435 .1450 .1462 .1472 .1480 .1486 .1489 .14908 .1066 .1099 .1130 .1160 .1188 .1215 .1240 .1263 .1284 .13049 .0723 .0757 .0791 .0825 .0858 .0891 .0923 .0954 .0985 .1014

10 .0441 .0469 .0498 .0528 .0558 .0558 .0618 .0649 .0679 .071011 .0245 .0265 .0285 .0307 .0330 .0353 .0377 .0401 .0426 .045212 .0124 .0137 .0150 .0164 .0179 .0194 .0210 .0227 .0245 .026213 .0058 .0065 .0073 .0081 .0089 .0098 .0108 .0119 .0130 .014214 .0025 .0029 .0033 .0037 .0041 .0046 .0052 .0058 .0064 .007115 .0010 .0012 .0014 .0016 .0018 .0020 .0023 .0026 .0029 .003316 .0004 .0005 .0005 .0006 .0007 .0008 .0010 .0011 .0013 .001417 .0001 .0002 .0002 .0002 .0003 .0003 .0004 .0004 .0005 .000618 .0000 .0001 .0001 .0001 .0001 .0001 .0001 .0002 .0002 .000219 .0000 .0000 .0000 .0000 .0000 .0000 .0001 .0001 .0001

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X 7.1 7.2 7.3 7.4 λ7.5 7.6 7.7 7.8 7.9 8.0

0 .0008 .0007 .0007 .0006 .0006 .0005 .0005 .0004 .0004 .00031 .0059 .0054 .0049 .0045 .0041 .0038 .0035 .0032 .0029 .00272 .0208 .0194 .0180 .0167 .0156 .0145 .0134 .0125 .0116 .01073 .0492 .0464 .0438 .0413 .0389 .0366 .0345 .0324 .0305 .02864 .0874 .0836 .0799 .0764 .0729 .0696 .0663 .0632 .0602 .05735 .1241 .1204 .1167 .1130 .1094 .1057 .1021 .0986 .0951 .09166 .1468 .1445 .1420 .1394 .1367 .1339 .1311 .1282 .1252 .12217 .1489 .1486 .1481 .1474 .1465 .1454 .1442 .1428 .1413 .13968 .1321 .1337 .1351 .1363 .1373 .1382 .1388 .1392 .1395 .13969 .1042 .1070 .1096 .1121 .1144 .1167 .1187 .1207 .1224 .1241

10 .0740 .0770 .0800 .0829 .0858 .0887 .0914 .0941 .0967 .099311 .0478 .0504 .0531 .0558 .0585 .0613 .0640 .0667 .0695 .072212 .0283 .0303 .0323 .0344 .0366 .0388 .0411 .0434 .0457 .048113 .0154 .0168 .0181 .0196 .0211 .0227 .0243 .0260 .0278 .029614 .0078 .0086 .0095 .0104 .0113 .0123 .0134 .0145 .0157 .016915 .0037 .0041 .0046 .0051 .0057 .0062 .0069 .0075 .0083 .009016 .0016 .0019 .0021 .0024 .0026 .0030 .0033 .0037 .0041 .004517 .0007 .0008 .0009 .0010 .0012 .0013 .0015 .0017 .0019 .002118 .0003 .0003 .0004 .0004 .0005 .0006 .0006 .0007 .0008 .000919 .0001 .0001 .0001 .0002 .0002 .0002 .0003 .0003 .0003 .000420 .0000 .0000 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .000221 .0000 .0000 .0000 .0000 .0000 .0000 .0001 .0001

X 8.1 8.2 8.3 8.4 λ

8.5 8.6 8.7 8.8 8.9 9.00 .0003 .0003 .0002 .0002 .0002 .0002 .0002 .0002 .0001 .00011 .0025 .0023 .0021 .0019 .0017 .0016 .0014 .0013 .0012 .00112 .0100 .0092 .0086 .0079 .0074 .0068 .0063 .0058 .0054 .00503 .0269 .0252 .0237 .0222 .0208 .0195 .0183 .0171 .0160 .01504 .0544 .0517 .0491 .0466 .0443 .0420 .0398 .0377 .0357 .03375 .0882 .0849 .0816 .0784 .0752 .0722 .0692 .0663 .0635 .06076 .1191 .1160 .1128 .1097 .1066 .1034 .1003 .0972 .0941 .09117 .1378 .1358 .1338 .1317 .1294 .1271 .1247 .1222 .1197 .11718 .1395 .1392 .1388 .1382 .1375 .1366 .1356 .1344 .1332 .13189 .1256 .1269 .1280 .1290 .1299 .1306 .1311 .1315 .1317 .1318

10 .1017 .1040 .1063 .1084 .1104 .1123 .1140 .1157 .1172 .118611 .0749 .0776 .0802 .0828 .0853 .0878 .0902 .0925 .0948 .097012 .0505 .0530 .0555 .0579 .0604 .0629 .0654 .0679 .0703 .072813 .0315 .0334 .0354 .0374 .0395 .0416 .0438 .0459 .0481 .050414 .0182 .0196 .0210 .0225 .0240 .0256 .0272 .0289 .0306 .032415 .0098 .0107 .0116 .0126 .0136 .0147 .0158 .0169 .0182 .019416 .0050 .0055 .0060 .0066 .0072 .0079 .0086 .0093 .0101 .010917 .0024 .0026 .0029 .0033 .0036 .0040 .0044 .0048 .0053 .005818 .0011 .0012 .0014 .0015 .0017 .0019 .0021 .0024 .0026 .002919 .0005 .0005 .0006 .0007 .0008 .0009 .0010 .0011 .0012 .001420 .0002 .0002 .0002 .0003 .0003 .0004 .0004 .0005 .0005 .000621 .0001 .0001 .0001 .0001 .0001 .0002 .0002 .0002 .0002 .000322 .0000 .0000 .0000 .0000 .0001 .0001 .0001 .0001 .0001 .0001

X 9.1 9.2 9.3 9.4 λ9.5 9.6 9.7 9.8 9.9 10.0

0 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .00001 .0010 .0009 .0009 .0008 .0007 .0007 .0006 .0005 .0005 .00052 .0046 .0043 .0040 .0037 .0034 .0031 .0029 .0027 .0025 .00233 .0140 .0131 .0123 .0115 .0107 .0100 .0093 .0087 .0081 .00764 .0319 .0302 .0285 .0269 .0254 .0240 .0226 .0213 .0201 .01895 .0581 .0555 .0530 .0506 .0483 .0460 .0439 .0418 .0398 .03786 .0881 .0851 .0822 .0793 .0764 .0736 .0709 .0682 .0656 .06317 .1145 .1118 .1091 .1064 .1037 .1010 .0982 .0955 .0928 .0901


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X 9.1 9.2 9.3 9.4 λ9.5 9.6 9.7 9.8 9.9 10.0

8 .1302 .1286 .1269 .1251 .1232 .1212 .1191 .1170 .1148 .11269 .1317 .1315 .1311 .1306 .1300 .1293 .1284 .1274 .1263 .1251

10 .1198 .1210 .1219 .1228 .1235 .1241 .1245 .1249 .1250 .125111 .0991 .1012 .1031 .1049 .1067 .1083 .1098 .1112 .1125 .113712 .0752 .0776 .0779 .0822 .0844 .0866 .0888 .0908 .0928 .094813 .0526 .0549 .0572 .0594 .0617 .0640 .0662 .0685 .0707 .072914 .0342 .0361 .0380 .0399 .0419 .0439 .0459 .0479 .0500 .052115 .0208 .0221 .0235 .0250 .0265 .0281 .0297 .0313 .0330 .034716 .0118 .0127 .0137 .0147 .0157 .0168 .0180 .0192 .0204 .021717 .0063 .0069 .0075 .0081 .0088 .0095 .0103 .0111 .0119 .012818 .0032 .0053 .0039 .0042 .0046 .0051 .0055 .0060 .0065 .007119 .0015 .0017 .0019 .0021 .0023 .0026 .0028 .0031 .0034 .003720 .0007 .0008 .0009 .0010 .0011 .0012 .0014 .0015 .0017 .001921 .0003 .0003 .0004 .0004 .0005 .0006 .0006 .0007 .0008 .000922 .0001 .0001 .0002 .0002 .0002 .0002 .0003 .0003 .0004 .000423 .0000 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0002 .000224 .0000 .0000 .0000 .0000 .0000 .0000 .0001 .0001 .0001

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Tabla 6.- Factores para las gráficas de control.

Tamaño de muestra

nc4

c5 d2 d3 D3 D4 A2

2 0.7979 0.6028 1.128 0.853 0 3.267 1.8803 0.8862 0.4633 1.693 0.888 0 2.574 1.0234 0.9213 0.3889 2.059 0.880 0 2.282 0.7295 0.9400 0.3412 2.326 0.864 0 2114 0.5776 0.9515 0.3076 2.534 0.848 0 2.004 0.4837 0.9594 0.2820 2.704 0.833 0.076 1.924 0.4198 0.9650 0.2622 2.847 0.820 0.136 1.864 1.3739 0.9693 0.2459 2.970 0.808 0.184 1.816 0.33710 0.9727 0.2321 3.078 0.797 0.223 1.777 0.30811 0.9754 0.2204 3.173 0.787 0.256 1.744 0.28512 0.9776 0.2105 3.258 0.778 0.283 1.717 0.26613 0.9794 0.2019 3.336 0.770 0.307 1.693 0.24914 0.9810 0.1940 3.407 0.763 0.328 1.672 0.23515 0.9823 0.1873 3.472 0.756 0.347 1.653 0.22316 0.9835 0.1809 3.532 0.750 0.363 1.637 0.21217 0.9845 0.1754 3.588 0.744 0.378 1.622 0.20318 0.9854 0.1703 3.640 0.739 0.391 1.608 0.19419 0.9862 0.1656 3.689 0.734 0.403 1.597 0.18720 0.9869 0.1613 3.735 0.729 0.415 1.585 0.18021 0.9876 0.1570 3.778 0.724 0.425 1.575 0.17322 0.9882 0.1532 3.819 0.720 0.434 1.566 0.16723 0.9887 0.1499 3.858 0.716 0.443 1.557 0.16224 0.9892 0.1466 3.895 0.712 0.451 1.548 0.15725 0.9896 0.1438 3.931 0.708 0.459 1.541 0.153


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Tabla 7.- Distribución normal estandarizada.La entrada representa el área debajo de la distribución normal estandarizada desde la media hasta Z.

Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .090.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .03590.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .07530.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .11410.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .15170.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .18790.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .22240.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .25490.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .28520.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .31330.9 .3159 .3186 .3213 .3238 .3264 .3289 .3315 .3340 .3365 .33891.0 .3413 .3438 .3461 .3845 .3508 .3531 .3554 .3577 .3599 .36211.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .38301.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .40151.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .41771.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .43191.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .44411.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .45451.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .46331.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .47061.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .47672.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .48172.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .48572.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .48902.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .49162.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .49362.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .49522.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .49642.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .49742.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .49812.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .49863.0 .49865 .49869 .49874 .49878 .49882 .49886 .49889 .49893 .49897 .499003.1 .49903 .49906 .49910 .49913 .49916 .49918 .49921 .49924 .49926 .499293.2 .49931 .49934 .49936 .49938 .49940 .49942 .49944 .49946 .49948 .499503.3 .49952 .49953 .49955 .49957 .49958 .49960 .49961 .49962 .49964 .499653.4 .49966 .49968 .49969 .49970 .49971 .49972 .49973 .49974 .49975 .499763.5 .49977 .49978 .49978 .49979 .49980 .49981 .49981 .49982 .49983 .499833.6 .49984 .49985 .49985 .49986 .49986 .49987 .49987 .49988 .49988 .499893.7 .49989 .49990 .49990 .49990 .49991 .49991 .49992 .49992 .49992 .499923.8 .49993 .49993 .49993 .49994 .49994 .49994 .49994 .49995 .49995 .499953.9 .49995 .49995 .49996 .49996 .49996 .49996 .49996 .49996 .49997 .49997

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Apéndice de Tablas

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