Pe Tabelas

Instituto Superior T´ecnico – Departamento de Matem´atica

Probabilidades e Estat´ıstica

Tabela 1: Fun¸ca˜o de distribui¸c˜ao Binomial FX (x) =

x   X n k=0

n x\p

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

k

pk (1 − p)n−k

0.09

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1

0 1

0.9900 0.9800 0.9700 0.9600 0.9500 0.9400 0.9300 0.9200 0.9100 0.9000 0.8500 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2

0 1 2

0.9801 0.9604 0.9409 0.9216 0.9025 0.8836 0.8649 0.8464 0.8281 0.8100 0.7225 0.6400 0.5625 0.4900 0.4225 0.3600 0.3025 0.2500 0.9999 0.9996 0.9991 0.9984 0.9975 0.9964 0.9951 0.9936 0.9919 0.9900 0.9775 0.9600 0.9375 0.9100 0.8775 0.8400 0.7975 0.7500 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3

0 1 2 3

0.9703 0.9412 0.9127 0.8847 0.9997 0.9988 0.9974 0.9953 1.0000 1.0000 1.0000 0.9999 1.0000

0.8574 0.9928 0.9999 1.0000

0.8306 0.9896 0.9998 1.0000

0.8044 0.9860 0.9997 1.0000

0.7787 0.9818 0.9995 1.0000

0.7536 0.9772 0.9993 1.0000

0.7290 0.9720 0.9990 1.0000

0.6141 0.9393 0.9966 1.0000

0.5120 0.8960 0.9920 1.0000

0.4219 0.8438 0.9844 1.0000

0.3430 0.7840 0.9730 1.0000

0.2746 0.7183 0.9571 1.0000

0.2160 0.6480 0.9360 1.0000

0.1664 0.5748 0.9089 1.0000

0.1250 0.5000 0.8750 1.0000

4

0 1 2 3 4

0.9606 0.9224 0.8853 0.8493 0.9994 0.9977 0.9948 0.9909 1.0000 1.0000 0.9999 0.9998 1.0000 1.0000

0.8145 0.9860 0.9995 1.0000

0.7807 0.9801 0.9992 1.0000

0.7481 0.9733 0.9987 1.0000

0.7164 0.9656 0.9981 1.0000

0.6857 0.9570 0.9973 0.9999 1.0000

0.6561 0.9477 0.9963 0.9999 1.0000

0.5220 0.8905 0.9880 0.9995 1.0000

0.4096 0.8192 0.9728 0.9984 1.0000

0.3164 0.7383 0.9492 0.9961 1.0000

0.2401 0.6517 0.9163 0.9919 1.0000

0.1785 0.5630 0.8735 0.9850 1.0000

0.1296 0.4752 0.8208 0.9744 1.0000

0.0915 0.3910 0.7585 0.9590 1.0000

0.0625 0.3125 0.6875 0.9375 1.0000

5

0 1 2 3 4 5

0.9510 0.9039 0.8587 0.8154 0.9990 0.9962 0.9915 0.9852 1.0000 0.9999 0.9997 0.9994 1.0000 1.0000 1.0000

0.7738 0.9774 0.9988 1.0000

0.7339 0.9681 0.9980 0.9999 1.0000

0.6957 0.9575 0.9969 0.9999 1.0000

0.6591 0.9456 0.9955 0.9998 1.0000

0.6240 0.9326 0.9937 0.9997 1.0000

0.5905 0.9185 0.9914 0.9995 1.0000

0.4437 0.8352 0.9734 0.9978 0.9999 1.0000

0.3277 0.7373 0.9421 0.9933 0.9997 1.0000

0.2373 0.6328 0.8965 0.9844 0.9990 1.0000

0.1681 0.5282 0.8369 0.9692 0.9976 1.0000

0.1160 0.4284 0.7648 0.9460 0.9947 1.0000

0.0778 0.3370 0.6826 0.9130 0.9898 1.0000

0.0503 0.2562 0.5931 0.8688 0.9815 1.0000

0.0313 0.1875 0.5000 0.8125 0.9688 1.0000

6

0 1 2 3 4 5 6

0.9415 0.8858 0.8330 0.7828 0.9985 0.9943 0.9875 0.9784 1.0000 0.9998 0.9995 0.9988 1.0000 1.0000 1.0000

0.7351 0.9672 0.9978 0.9999 1.0000

0.6899 0.9541 0.9962 0.9998 1.0000

0.6470 0.9392 0.9942 0.9997 1.0000

0.6064 0.9227 0.9915 0.9995 1.0000

0.5679 0.9048 0.9882 0.9992 1.0000

0.5314 0.8857 0.9842 0.9987 0.9999 1.0000

0.3771 0.7765 0.9527 0.9941 0.9996 1.0000

0.2621 0.6554 0.9011 0.9830 0.9984 0.9999 1.0000

0.1780 0.5339 0.8306 0.9624 0.9954 0.9998 1.0000

0.1176 0.4202 0.7443 0.9295 0.9891 0.9993 1.0000

0.0754 0.3191 0.6471 0.8826 0.9777 0.9982 1.0000

0.0467 0.2333 0.5443 0.8208 0.9590 0.9959 1.0000

0.0277 0.1636 0.4415 0.7447 0.9308 0.9917 1.0000

0.0156 0.1094 0.3438 0.6563 0.8906 0.9844 1.0000

7

0 1 2 3 4 5 6 7

0.9321 0.8681 0.8080 0.7514 0.9980 0.9921 0.9829 0.9706 1.0000 0.9997 0.9991 0.9980 1.0000 1.0000 0.9999 1.0000

0.6983 0.9556 0.9962 0.9998 1.0000

0.6485 0.9382 0.9937 0.9996 1.0000

0.6017 0.9187 0.9903 0.9993 1.0000

0.5578 0.8974 0.9860 0.9988 0.9999 1.0000

0.5168 0.8745 0.9807 0.9982 0.9999 1.0000

0.4783 0.8503 0.9743 0.9973 0.9998 1.0000

0.3206 0.7166 0.9262 0.9879 0.9988 0.9999 1.0000

0.2097 0.5767 0.8520 0.9667 0.9953 0.9996 1.0000

0.1335 0.4449 0.7564 0.9294 0.9871 0.9987 0.9999 1.0000

0.0824 0.3294 0.6471 0.8740 0.9712 0.9962 0.9998 1.0000

0.0490 0.2338 0.5323 0.8002 0.9444 0.9910 0.9994 1.0000

0.0280 0.1586 0.4199 0.7102 0.9037 0.9812 0.9984 1.0000

0.0152 0.1024 0.3164 0.6083 0.8471 0.9643 0.9963 1.0000

0.0078 0.0625 0.2266 0.5000 0.7734 0.9375 0.9922 1.0000

8

0 1 2 3 4 5 6 7 8

0.9227 0.9973 0.9999 1.0000

0.8508 0.9897 0.9996 1.0000

0.7837 0.9777 0.9987 0.9999 1.0000

0.7214 0.9619 0.9969 0.9998 1.0000

0.6634 0.9428 0.9942 0.9996 1.0000

0.6096 0.9208 0.9904 0.9993 1.0000

0.5596 0.8965 0.9853 0.9987 0.9999 1.0000

0.5132 0.8702 0.9789 0.9978 0.9999 1.0000

0.4703 0.8423 0.9711 0.9966 0.9997 1.0000

0.4305 0.8131 0.9619 0.9950 0.9996 1.0000

0.2725 0.6572 0.8948 0.9786 0.9971 0.9998 1.0000

0.1678 0.5033 0.7969 0.9437 0.9896 0.9988 0.9999 1.0000

0.1001 0.3671 0.6785 0.8862 0.9727 0.9958 0.9996 1.0000

0.0576 0.2553 0.5518 0.8059 0.9420 0.9887 0.9987 0.9999 1.0000

0.0319 0.1691 0.4278 0.7064 0.8939 0.9747 0.9964 0.9998 1.0000

0.0168 0.1064 0.3154 0.5941 0.8263 0.9502 0.9915 0.9993 1.0000

0.0084 0.0632 0.2201 0.4770 0.7396 0.9115 0.9819 0.9983 1.0000

0.0039 0.0352 0.1445 0.3633 0.6367 0.8555 0.9648 0.9961 1.0000

9

0 1 2 3 4 5 6 7 8 9

0.9135 0.9966 0.9999 1.0000

0.8337 0.9869 0.9994 1.0000

0.7602 0.9718 0.9980 0.9999 1.0000

0.6925 0.9522 0.9955 0.9997 1.0000

0.6302 0.9288 0.9916 0.9994 1.0000

0.5730 0.9022 0.9862 0.9987 0.9999 1.0000

0.5204 0.8729 0.9791 0.9977 0.9998 1.0000

0.4722 0.8417 0.9702 0.9963 0.9997 1.0000

0.4279 0.8088 0.9595 0.9943 0.9995 1.0000

0.3874 0.7748 0.9470 0.9917 0.9991 0.9999 1.0000

0.2316 0.5995 0.8591 0.9661 0.9944 0.9994 1.0000

0.1342 0.4362 0.7382 0.9144 0.9804 0.9969 0.9997 1.0000

0.0751 0.3003 0.6007 0.8343 0.9511 0.9900 0.9987 0.9999 1.0000

0.0404 0.1960 0.4628 0.7297 0.9012 0.9747 0.9957 0.9996 1.0000

0.0207 0.1211 0.3373 0.6089 0.8283 0.9464 0.9888 0.9986 0.9999 1.0000

0.0101 0.0705 0.2318 0.4826 0.7334 0.9006 0.9750 0.9962 0.9997 1.0000

0.0046 0.0385 0.1495 0.3614 0.6214 0.8342 0.9502 0.9909 0.9992 1.0000

0.0020 0.0195 0.0898 0.2539 0.5000 0.7461 0.9102 0.9805 0.9980 1.0000

1

n x\p

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

10

0 1 2 3 4 5 6 7 8 9 10

0.9044 0.9957 0.9999 1.0000

0.8171 0.9838 0.9991 1.0000

0.7374 0.9655 0.9972 0.9999 1.0000

0.6648 0.9418 0.9938 0.9996 1.0000

0.5987 0.9139 0.9885 0.9990 0.9999 1.0000

0.5386 0.8824 0.9812 0.9980 0.9998 1.0000

0.4840 0.8483 0.9717 0.9964 0.9997 1.0000

0.4344 0.8121 0.9599 0.9942 0.9994 1.0000

0.3894 0.7746 0.9460 0.9912 0.9990 0.9999 1.0000

0.3487 0.7361 0.9298 0.9872 0.9984 0.9999 1.0000

0.1969 0.5443 0.8202 0.9500 0.9901 0.9986 0.9999 1.0000

0.1074 0.3758 0.6778 0.8791 0.9672 0.9936 0.9991 0.9999 1.0000

0.0563 0.2440 0.5256 0.7759 0.9219 0.9803 0.9965 0.9996 1.0000

0.0282 0.1493 0.3828 0.6496 0.8497 0.9527 0.9894 0.9984 0.9999 1.0000

0.0135 0.0860 0.2616 0.5138 0.7515 0.9051 0.9740 0.9952 0.9995 1.0000

0.0060 0.0464 0.1673 0.3823 0.6331 0.8338 0.9452 0.9877 0.9983 0.9999 1.0000

0.0025 0.0233 0.0996 0.2660 0.5044 0.7384 0.8980 0.9726 0.9955 0.9997 1.0000

0.0010 0.0107 0.0547 0.1719 0.3770 0.6230 0.8281 0.9453 0.9893 0.9990 1.0000

11

0 1 2 3 4 5 6 7 8 9 10 11

0.8953 0.9948 0.9998 1.0000

0.8007 0.9805 0.9988 1.0000

0.7153 0.9587 0.9963 0.9998 1.0000

0.6382 0.9308 0.9917 0.9993 1.0000

0.5688 0.8981 0.9848 0.9984 0.9999 1.0000

0.5063 0.8618 0.9752 0.9970 0.9997 1.0000

0.4501 0.8228 0.9630 0.9947 0.9995 1.0000

0.3996 0.7819 0.9481 0.9915 0.9990 0.9999 1.0000

0.3544 0.7399 0.9305 0.9871 0.9983 0.9998 1.0000

0.3138 0.6974 0.9104 0.9815 0.9972 0.9997 1.0000

0.1673 0.4922 0.7788 0.9306 0.9841 0.9973 0.9997 1.0000

0.0859 0.3221 0.6174 0.8389 0.9496 0.9883 0.9980 0.9998 1.0000

0.0422 0.1971 0.4552 0.7133 0.8854 0.9657 0.9924 0.9988 0.9999 1.0000

0.0198 0.1130 0.3127 0.5696 0.7897 0.9218 0.9784 0.9957 0.9994 1.0000

0.0088 0.0606 0.2001 0.4256 0.6683 0.8513 0.9499 0.9878 0.9980 0.9998 1.0000

0.0036 0.0302 0.1189 0.2963 0.5328 0.7535 0.9006 0.9707 0.9941 0.9993 1.0000

0.0014 0.0139 0.0652 0.1911 0.3971 0.6331 0.8262 0.9390 0.9852 0.9978 0.9998 1.0000

0.0005 0.0059 0.0327 0.1133 0.2744 0.5000 0.7256 0.8867 0.9673 0.9941 0.9995 1.0000

12

0 1 2 3 4 5 6 7 8 9 10 11 12

0.8864 0.9938 0.9998 1.0000

0.7847 0.9769 0.9985 0.9999 1.0000

0.6938 0.9514 0.9952 0.9997 1.0000

0.6127 0.9191 0.9893 0.9990 0.9999 1.0000

0.5404 0.8816 0.9804 0.9978 0.9998 1.0000

0.4759 0.8405 0.9684 0.9957 0.9996 1.0000

0.4186 0.7967 0.9532 0.9925 0.9991 0.9999 1.0000

0.3677 0.7513 0.9348 0.9880 0.9984 0.9998 1.0000

0.3225 0.7052 0.9134 0.9820 0.9973 0.9997 1.0000

0.2824 0.6590 0.8891 0.9744 0.9957 0.9995 0.9999 1.0000

0.1422 0.4435 0.7358 0.9078 0.9761 0.9954 0.9993 0.9999 1.0000

0.0687 0.2749 0.5583 0.7946 0.9274 0.9806 0.9961 0.9994 0.9999 1.0000

0.0317 0.1584 0.3907 0.6488 0.8424 0.9456 0.9857 0.9972 0.9996 1.0000

0.0138 0.0850 0.2528 0.4925 0.7237 0.8822 0.9614 0.9905 0.9983 0.9998 1.0000

0.0057 0.0424 0.1513 0.3467 0.5833 0.7873 0.9154 0.9745 0.9944 0.9992 0.9999 1.0000

0.0022 0.0196 0.0834 0.2253 0.4382 0.6652 0.8418 0.9427 0.9847 0.9972 0.9997 1.0000

0.0008 0.0083 0.0421 0.1345 0.3044 0.5269 0.7393 0.8883 0.9644 0.9921 0.9989 0.9999 1.0000

0.0002 0.0032 0.0193 0.0730 0.1938 0.3872 0.6128 0.8062 0.9270 0.9807 0.9968 0.9998 1.0000

13

0 1 2 3 4 5 6 7 8 9 10 11 12 13

0.8775 0.9928 0.9997 1.0000

0.7690 0.9730 0.9980 0.9999 1.0000

0.6730 0.9436 0.9938 0.9995 1.0000

0.5882 0.9068 0.9865 0.9986 0.9999 1.0000

0.5133 0.8646 0.9755 0.9969 0.9997 1.0000

0.4474 0.8186 0.9608 0.9940 0.9993 0.9999 1.0000

0.3893 0.7702 0.9422 0.9897 0.9987 0.9999 1.0000

0.3383 0.7206 0.9201 0.9837 0.9976 0.9997 1.0000

0.2935 0.6707 0.8946 0.9758 0.9959 0.9995 0.9999 1.0000

0.2542 0.6213 0.8661 0.9658 0.9935 0.9991 0.9999 1.0000

0.1209 0.3983 0.6920 0.8820 0.9658 0.9925 0.9987 0.9998 1.0000

0.0550 0.2336 0.5017 0.7473 0.9009 0.9700 0.9930 0.9988 0.9998 1.0000

0.0238 0.1267 0.3326 0.5843 0.7940 0.9198 0.9757 0.9944 0.9990 0.9999 1.0000

0.0097 0.0637 0.2025 0.4206 0.6543 0.8346 0.9376 0.9818 0.9960 0.9993 0.9999 1.0000

0.0037 0.0296 0.1132 0.2783 0.5005 0.7159 0.8705 0.9538 0.9874 0.9975 0.9997 1.0000

0.0013 0.0126 0.0579 0.1686 0.3530 0.5744 0.7712 0.9023 0.9679 0.9922 0.9987 0.9999 1.0000

0.0004 0.0049 0.0269 0.0929 0.2279 0.4268 0.6437 0.8212 0.9302 0.9797 0.9959 0.9995 1.0000

0.0001 0.0017 0.0112 0.0461 0.1334 0.2905 0.5000 0.7095 0.8666 0.9539 0.9888 0.9983 0.9999 1.0000

14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.8687 0.9916 0.9997 1.0000

0.7536 0.9690 0.9975 0.9999 1.0000

0.6528 0.9355 0.9923 0.9994 1.0000

0.5647 0.8941 0.9833 0.9981 0.9998 1.0000

0.4877 0.8470 0.9699 0.9958 0.9996 1.0000

0.4205 0.7963 0.9522 0.9920 0.9990 0.9999 1.0000

0.3620 0.7436 0.9302 0.9864 0.9980 0.9998 1.0000

0.3112 0.6900 0.9042 0.9786 0.9965 0.9996 1.0000

0.2670 0.6368 0.8745 0.9685 0.9941 0.9992 0.9999 1.0000

0.2288 0.5846 0.8416 0.9559 0.9908 0.9985 0.9998 1.0000

0.1028 0.3567 0.6479 0.8535 0.9533 0.9885 0.9978 0.9997 1.0000

0.0440 0.1979 0.4481 0.6982 0.8702 0.9561 0.9884 0.9976 0.9996 1.0000

0.0178 0.1010 0.2811 0.5213 0.7415 0.8883 0.9617 0.9897 0.9978 0.9997 1.0000

0.0068 0.0475 0.1608 0.3552 0.5842 0.7805 0.9067 0.9685 0.9917 0.9983 0.9998 1.0000

0.0024 0.0205 0.0839 0.2205 0.4227 0.6405 0.8164 0.9247 0.9757 0.9940 0.9989 0.9999 1.0000

0.0008 0.0081 0.0398 0.1243 0.2793 0.4859 0.6925 0.8499 0.9417 0.9825 0.9961 0.9994 0.9999 1.0000

0.0002 0.0029 0.0170 0.0632 0.1672 0.3373 0.5461 0.7414 0.8811 0.9574 0.9886 0.9978 0.9997 1.0000

0.0001 0.0009 0.0065 0.0287 0.0898 0.2120 0.3953 0.6047 0.7880 0.9102 0.9713 0.9935 0.9991 0.9999 1.0000

15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.8601 0.9904 0.9996 1.0000

0.7386 0.9647 0.9970 0.9998 1.0000

0.6333 0.9270 0.9906 0.9992 0.9999 1.0000

0.5421 0.8809 0.9797 0.9976 0.9998 1.0000

0.4633 0.8290 0.9638 0.9945 0.9994 0.9999 1.0000

0.3953 0.7738 0.9429 0.9896 0.9986 0.9999 1.0000

0.3367 0.7168 0.9171 0.9825 0.9972 0.9997 1.0000

0.2863 0.6597 0.8870 0.9727 0.9950 0.9993 0.9999 1.0000

0.2430 0.6035 0.8531 0.9601 0.9918 0.9987 0.9998 1.0000

0.2059 0.5490 0.8159 0.9444 0.9873 0.9978 0.9997 1.0000

0.0874 0.3186 0.6042 0.8227 0.9383 0.9832 0.9964 0.9994 0.9999 1.0000

0.0352 0.1671 0.3980 0.6482 0.8358 0.9389 0.9819 0.9958 0.9992 0.9999 1.0000

0.0134 0.0802 0.2361 0.4613 0.6865 0.8516 0.9434 0.9827 0.9958 0.9992 0.9999 1.0000

0.0047 0.0353 0.1268 0.2969 0.5155 0.7216 0.8689 0.9500 0.9848 0.9963 0.9993 0.9999 1.0000

0.0016 0.0142 0.0617 0.1727 0.3519 0.5643 0.7548 0.8868 0.9578 0.9876 0.9972 0.9995 0.9999 1.0000

0.0005 0.0052 0.0271 0.0905 0.2173 0.4032 0.6098 0.7869 0.9050 0.9662 0.9907 0.9981 0.9997 1.0000

0.0001 0.0017 0.0107 0.0424 0.1204 0.2608 0.4522 0.6535 0.8182 0.9231 0.9745 0.9937 0.9989 0.9999 1.0000

0.0000 0.0005 0.0037 0.0176 0.0592 0.1509 0.3036 0.5000 0.6964 0.8491 0.9408 0.9824 0.9963 0.9995 1.0000

2

n x\p

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.8515 0.9891 0.9995 1.0000

0.7238 0.9601 0.9963 0.9998 1.0000

0.6143 0.9182 0.9887 0.9989 0.9999 1.0000

0.5204 0.8673 0.9758 0.9968 0.9997 1.0000

0.4401 0.8108 0.9571 0.9930 0.9991 0.9999 1.0000

0.3716 0.7511 0.9327 0.9868 0.9981 0.9998 1.0000

0.3131 0.6902 0.9031 0.9779 0.9962 0.9995 0.9999 1.0000

0.2634 0.6299 0.8689 0.9658 0.9932 0.9990 0.9999 1.0000

0.2211 0.5711 0.8306 0.9504 0.9889 0.9981 0.9997 1.0000

0.1853 0.5147 0.7892 0.9316 0.9830 0.9967 0.9995 0.9999 1.0000

0.0743 0.2839 0.5614 0.7899 0.9209 0.9765 0.9944 0.9989 0.9998 1.0000

0.0281 0.1407 0.3518 0.5981 0.7982 0.9183 0.9733 0.9930 0.9985 0.9998 1.0000

0.0100 0.0635 0.1971 0.4050 0.6302 0.8103 0.9204 0.9729 0.9925 0.9984 0.9997 1.0000

0.0033 0.0261 0.0994 0.2459 0.4499 0.6598 0.8247 0.9256 0.9743 0.9929 0.9984 0.9997 1.0000

0.0010 0.0098 0.0451 0.1339 0.2892 0.4900 0.6881 0.8406 0.9329 0.9771 0.9938 0.9987 0.9998 1.0000

0.0003 0.0033 0.0183 0.0651 0.1666 0.3288 0.5272 0.7161 0.8577 0.9417 0.9809 0.9951 0.9991 0.9999 1.0000

0.0001 0.0010 0.0066 0.0281 0.0853 0.1976 0.3660 0.5629 0.7441 0.8759 0.9514 0.9851 0.9965 0.9994 0.9999 1.0000

0.0000 0.0003 0.0021 0.0106 0.0384 0.1051 0.2272 0.4018 0.5982 0.7728 0.8949 0.9616 0.9894 0.9979 0.9997 1.0000

17

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.8429 0.9877 0.9994 1.0000

0.7093 0.9554 0.9956 0.9997 1.0000

0.5958 0.9091 0.9866 0.9986 0.9999 1.0000

0.4996 0.8535 0.9714 0.9960 0.9996 1.0000

0.4181 0.7922 0.9497 0.9912 0.9988 0.9999 1.0000

0.3493 0.7283 0.9218 0.9836 0.9974 0.9997 1.0000

0.2912 0.6638 0.8882 0.9727 0.9949 0.9993 0.9999 1.0000

0.2423 0.6005 0.8497 0.9581 0.9911 0.9985 0.9998 1.0000

0.2012 0.5396 0.8073 0.9397 0.9855 0.9973 0.9996 1.0000

0.1668 0.4818 0.7618 0.9174 0.9779 0.9953 0.9992 0.9999 1.0000

0.0631 0.2525 0.5198 0.7556 0.9013 0.9681 0.9917 0.9983 0.9997 1.0000

0.0225 0.1182 0.3096 0.5489 0.7582 0.8943 0.9623 0.9891 0.9974 0.9995 0.9999 1.0000

0.0075 0.0501 0.1637 0.3530 0.5739 0.7653 0.8929 0.9598 0.9876 0.9969 0.9994 0.9999 1.0000

0.0023 0.0193 0.0774 0.2019 0.3887 0.5968 0.7752 0.8954 0.9597 0.9873 0.9968 0.9993 0.9999 1.0000

0.0007 0.0067 0.0327 0.1028 0.2348 0.4197 0.6188 0.7872 0.9006 0.9617 0.9880 0.9970 0.9994 0.9999 1.0000

0.0002 0.0021 0.0123 0.0464 0.1260 0.2639 0.4478 0.6405 0.8011 0.9081 0.9652 0.9894 0.9975 0.9995 0.9999 1.0000

0.0000 0.0006 0.0041 0.0184 0.0596 0.1471 0.2902 0.4743 0.6626 0.8166 0.9174 0.9699 0.9914 0.9981 0.9997 1.0000

0.0000 0.0001 0.0012 0.0064 0.0245 0.0717 0.1662 0.3145 0.5000 0.6855 0.8338 0.9283 0.9755 0.9936 0.9988 0.9999 1.0000

18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.8262 0.9847 0.9991 1.0000

0.6951 0.9505 0.9948 0.9996 1.0000

0.5606 0.8900 0.9817 0.9978 0.9998 1.0000

0.4796 0.8393 0.9667 0.9950 0.9994 0.9999 1.0000

0.3774 0.7547 0.9335 0.9868 0.9980 0.9998 1.0000

0.3283 0.7055 0.9102 0.9799 0.9966 0.9995 1.0000

0.2708 0.6378 0.8725 0.9667 0.9933 0.9990 0.9999 1.0000

0.2051 0.5440 0.8092 0.9398 0.9853 0.9971 0.9996 0.9999 1.0000

0.1831 0.5091 0.7832 0.9277 0.9814 0.9962 0.9994 0.9999 1.0000

0.1351 0.4203 0.7054 0.8850 0.9648 0.9914 0.9983 0.9997 1.0000

0.0456 0.1985 0.4413 0.6841 0.8556 0.9463 0.9837 0.9959 0.9992 0.9999 1.0000

0.0144 0.0829 0.2369 0.4551 0.6733 0.8369 0.9324 0.9767 0.9933 0.9984 0.9997 1.0000

0.0042 0.0310 0.1113 0.2631 0.4654 0.6678 0.8251 0.9225 0.9713 0.9911 0.9977 0.9995 0.9999 1.0000

0.0011 0.0104 0.0462 0.1332 0.2822 0.4739 0.6655 0.8180 0.9161 0.9674 0.9895 0.9972 0.9994 0.9999 1.0000

0.0004 0.0046 0.0236 0.0783 0.1886 0.3550 0.5491 0.7283 0.8609 0.9403 0.9788 0.9938 0.9986 0.9997 1.0000

0.0001 0.0008 0.0055 0.0230 0.0696 0.1629 0.3081 0.4878 0.6675 0.8139 0.9115 0.9648 0.9884 0.9969 0.9994 0.9999 1.0000

0.0000 0.0003 0.0025 0.0120 0.0411 0.1077 0.2258 0.3915 0.5778 0.7473 0.8720 0.9463 0.9817 0.9951 0.9990 0.9999 1.0000

0.0000 0.0000 0.0004 0.0022 0.0096 0.0318 0.0835 0.1796 0.3238 0.5000 0.6762 0.8204 0.9165 0.9682 0.9904 0.9978 0.9996 1.0000

19

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.8262 0.9847 0.9991 1.0000

0.6812 0.9454 0.9939 0.9995 1.0000

0.5606 0.8900 0.9817 0.9978 0.9998 1.0000

0.4604 0.8249 0.9616 0.9939 0.9993 0.9999 1.0000

0.3774 0.7547 0.9335 0.9868 0.9980 0.9998 1.0000

0.3086 0.6829 0.8979 0.9757 0.9956 0.9994 0.9999 1.0000

0.2519 0.6121 0.8561 0.9602 0.9915 0.9986 0.9998 1.0000

0.2051 0.5440 0.8092 0.9398 0.9853 0.9971 0.9996 0.9999 1.0000

0.1666 0.4798 0.7585 0.9147 0.9765 0.9949 0.9991 0.9999 1.0000

0.1351 0.4203 0.7054 0.8850 0.9648 0.9914 0.9983 0.9997 1.0000

0.0456 0.1985 0.4413 0.6841 0.8556 0.9463 0.9837 0.9959 0.9992 0.9999 1.0000

0.0144 0.0829 0.2369 0.4551 0.6733 0.8369 0.9324 0.9767 0.9933 0.9984 0.9997 1.0000

0.0042 0.0310 0.1113 0.2631 0.4654 0.6678 0.8251 0.9225 0.9713 0.9911 0.9977 0.9995 0.9999 1.0000

0.0011 0.0104 0.0462 0.1332 0.2822 0.4739 0.6655 0.8180 0.9161 0.9674 0.9895 0.9972 0.9994 0.9999 1.0000

0.0003 0.0031 0.0170 0.0591 0.1500 0.2968 0.4812 0.6656 0.8145 0.9125 0.9653 0.9886 0.9969 0.9993 0.9999 1.0000

0.0001 0.0008 0.0055 0.0230 0.0696 0.1629 0.3081 0.4878 0.6675 0.8139 0.9115 0.9648 0.9884 0.9969 0.9994 0.9999 1.0000

0.0000 0.0002 0.0015 0.0077 0.0280 0.0777 0.1727 0.3169 0.4940 0.6710 0.8159 0.9129 0.9658 0.9891 0.9972 0.9995 0.9999 1.0000

0.0000 0.0000 0.0004 0.0022 0.0096 0.0318 0.0835 0.1796 0.3238 0.5000 0.6762 0.8204 0.9165 0.9682 0.9904 0.9978 0.9996 1.0000

20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.8179 0.9831 0.9990 1.0000

0.6676 0.9401 0.9929 0.9994 1.0000

0.5438 0.8802 0.9790 0.9973 0.9997 1.0000

0.4420 0.8103 0.9561 0.9926 0.9990 0.9999 1.0000

0.3585 0.7358 0.9245 0.9841 0.9974 0.9997 1.0000

0.2901 0.6605 0.8850 0.9710 0.9944 0.9991 0.9999 1.0000

0.2342 0.5869 0.8390 0.9529 0.9893 0.9981 0.9997 1.0000

0.1887 0.5169 0.7879 0.9294 0.9817 0.9962 0.9994 0.9999 1.0000

0.1516 0.4516 0.7334 0.9007 0.9710 0.9932 0.9987 0.9998 1.0000

0.1216 0.3917 0.6769 0.8670 0.9568 0.9887 0.9976 0.9996 0.9999 1.0000

0.0388 0.1756 0.4049 0.6477 0.8298 0.9327 0.9781 0.9941 0.9987 0.9998 1.0000

0.0115 0.0692 0.2061 0.4114 0.6296 0.8042 0.9133 0.9679 0.9900 0.9974 0.9994 0.9999 1.0000

0.0032 0.0243 0.0913 0.2252 0.4148 0.6172 0.7858 0.8982 0.9591 0.9861 0.9961 0.9991 0.9998 1.0000

0.0008 0.0076 0.0355 0.1071 0.2375 0.4164 0.6080 0.7723 0.8867 0.9520 0.9829 0.9949 0.9987 0.9997 1.0000

0.0002 0.0021 0.0121 0.0444 0.1182 0.2454 0.4166 0.6010 0.7624 0.8782 0.9468 0.9804 0.9940 0.9985 0.9997 1.0000

0.0000 0.0005 0.0036 0.0160 0.0510 0.1256 0.2500 0.4159 0.5956 0.7553 0.8725 0.9435 0.9790 0.9935 0.9984 0.9997 1.0000

0.0000 0.0001 0.0009 0.0049 0.0189 0.0553 0.1299 0.2520 0.4143 0.5914 0.7507 0.8692 0.9420 0.9786 0.9936 0.9985 0.9997 1.0000

0.0000 0.0000 0.0002 0.0013 0.0059 0.0207 0.0577 0.1316 0.2517 0.4119 0.5881 0.7483 0.8684 0.9423 0.9793 0.9941 0.9987 0.9998 1.0000

3

Tabela 2: Fun¸ca˜o de distribui¸c˜ao de Poisson FX (x) =

x X

e−λ λk k!

k=0

λ

0

1

2

0.01 0.02 0.03 0.04 0.05

0.9900 0.9802 0.9704 0.9608 0.9512

1.0000 0.9998 0.9996 0.9992 0.9988

1.0000 1.0000 1.0000 1.0000

0.06 0.07 0.08 0.09 0.10

0.9418 0.9324 0.9231 0.9139 0.9048

0.9983 0.9977 0.9970 0.9962 0.9953

1.0000 0.9999 0.9999 0.9999 0.9998

1.0000 1.0000 1.0000 1.0000

0.15 0.20 0.25 0.30 0.35 0.40 0.45

0.8607 0.8187 0.7788 0.7408 0.7047 0.6703 0.6376

0.9898 0.9825 0.9735 0.9631 0.9513 0.9384 0.9246

0.9995 0.9989 0.9978 0.9964 0.9945 0.9921 0.9891

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

0.6065 0.5769 0.5488 0.5220 0.4966 0.4724 0.4493 0.4274 0.4066 0.3867

0.9098 0.8943 0.8781 0.8614 0.8442 0.8266 0.8088 0.7907 0.7725 0.7541

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90

0.3679 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0 0 10 0 10 0 10 0 10

2.00 2.20 2.40 2.60 2.80

3.00 3.20 3.40 3.60 3.80

4.00 4.20 4.40 4.60 4.80

5.00 5.20 5.40 5.60 5.80

x

3

4

5

6

7

8

9

1.0000 0.9999 0.9999 0.9997 0.9995 0.9992 0.9988

1.0000 1.0000 1.0000 1.0000 0.9999 0.9999

1.0000 1.0000

0.9856 0.9815 0.9769 0.9717 0.9659 0.9595 0.9526 0.9451 0.9371 0.9287

0.9982 0.9975 0.9966 0.9956 0.9942 0.9927 0.9909 0.9889 0.9865 0.9839

0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 0.9986 0.9982 0.9977 0.9971

1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9997 0.9997 0.9995

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999

1.0000

0.7358 0.6990 0.6626 0.6268 0.5918 0.5578 0.5249 0.4932 0.4628 0.4337

0.9197 0.9004 0.8795 0.8571 0.8335 0.8088 0.7834 0.7572 0.7306 0.7037

0.9810 0.9743 0.9662 0.9569 0.9463 0.9344 0.9212 0.9068 0.8913 0.8747

0.9963 0.9946 0.9923 0.9893 0.9857 0.9814 0.9763 0.9704 0.9636 0.9559

0.9994 0.9990 0.9985 0.9978 0.9968 0.9955 0.9940 0.9920 0.9896 0.9868

0.9999 0.9999 0.9997 0.9996 0.9994 0.9991 0.9987 0.9981 0.9974 0.9966

1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992

1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998

1.0000 1.0000 1.0000

0.1353 0.1108 1.0000 0.0907 1.0000 0.0743 0.9999 0.0608 0.9998

0.4060 0.3546

0.6767 0.6227

0.8571 0.8194

0.9473 0.9275

0.9834 0.9751

0.9955 0.9925

0.9989 0.9980

0.9998 0.9995

1.0000 0.9999

0.3084

0.5697

0.7787

0.9041

0.9643

0.9884

0.9967

0.9991

0.9998

0.2674 1.0000 0.2311 1.0000

0.5184

0.7360

0.8774

0.9510

0.9828

0.9947

0.9985

0.9996

0.4695

0.6919

0.8477

0.9349

0.9756

0.9919

0.9976

0.9993

0 10 0 10 0 10 0 10 0 10

0.0498 0.9997 0.0408 0.9995 0.0334 0.9992 0.0273 0.9987 0.0224 0.9981

0.1991 0.9999 0.1712 0.9999 0.1468 0.9998 0.1257 0.9996 0.1074 0.9994

0.4232 1.0000 0.3799 1.0000 0.3397 0.9999 0.3027 0.9999 0.2689 0.9998

0.6472

0.8153

0.9161

0.9665

0.9881

0.9962

0.9989

0.6025

0.7806

0.8946

0.9554

0.9832

0.9943

0.9982

0.5584 1.0000 0.5152 1.0000 0.4735 1.0000

0.7442

0.8705

0.9421

0.9769

0.9917

0.9973

0.7064

0.8441

0.9267

0.9692

0.9883

0.9960

0.6678

0.8156

0.9091

0.9599

0.9840

0.9942

0 10 0 10 0 10 0 10 0 10

0.0183 0.9972 0.0150 0.9959 0.0123 0.9943 0.0101 0.9922 0.0082 0.9896

0.0916 0.9991 0.0780 0.9986 0.0663 0.9980 0.0563 0.9971 0.0477 0.9960

0.2381 0.9997 0.2102 0.9996 0.1851 0.9993 0.1626 0.9990 0.1425 0.9986

0.4335 0.9999 0.3954 0.9999 0.3594 0.9998 0.3257 0.9997 0.2942 0.9995

0.6288 1.0000 0.5898 1.0000 0.5512 0.9999 0.5132 0.9999 0.4763 0.9999

0.7851

0.8893

0.9489

0.9786

0.9919

0.7531

0.8675

0.9361

0.9721

0.9889

0.7199 1.0000 0.6858 1.0000 0.6510 1.0000

0.8436

0.9214

0.9642

0.9851

0.8180

0.9049

0.9549

0.9805

0.7908

0.8867

0.9442

0.9749

0 10 0 10 0 10 0 10 0 10

0.0067 0.9863 0.0055 0.9823 0.0045 0.9775 0.0037 0.9718 0.0030 0.9651

0.0404 0.9945 0.0342 0.9927 0.0289 0.9904 0.0244 0.9875 0.0206 0.9841

0.1247 0.9980 0.1088 0.9972 0.0948 0.9962 0.0824 0.9949 0.0715 0.9932

0.2650 0.9993 0.2381 0.9990 0.2133 0.9986 0.1906 0.9980 0.1700 0.9973

0.4405 0.9998 0.4061 0.9997 0.3733 0.9995 0.3422 0.9993 0.3127 0.9990

0.6160 0.9999 0.5809 0.9999 0.5461 0.9998 0.5119 0.9998 0.4783 0.9996

0.7622 1.0000 0.7324 1.0000 0.7017 0.9999 0.6703 0.9999 0.6384 0.9999

0.8666

0.9319

0.9682

0.8449

0.9181

0.9603

0.8217 1.0000 0.7970 1.0000 0.7710 1.0000

0.9027

0.9512

0.8857

0.9409

0.8672

0.9292

4

λ

x

0

1

2

3

4

5

6

7

8

9

6.00

0 10 0 10 0 10 0 10 0 10

0.0025 0.9574 0.0020 0.9486 0.0017 0.9386 0.0014 0.9274 0.0011 0.9151

0.0174 0.9799 0.0146 0.9750 0.0123 0.9693 0.0103 0.9627 0.0087 0.9552

0.0620 0.9912 0.0536 0.9887 0.0463 0.9857 0.0400 0.9821 0.0344 0.9779

0.1512 0.9964 0.1342 0.9952 0.1189 0.9937 0.1052 0.9920 0.0928 0.9898

0.2851 0.9986 0.2592 0.9981 0.2351 0.9974 0.2127 0.9966 0.1920 0.9956

0.4457 0.9995 0.4141 0.9993 0.3837 0.9990 0.3547 0.9986 0.3270 0.9982

0.6063 0.9998 0.5742 0.9997 0.5423 0.9996 0.5108 0.9995 0.4799 0.9993

0.7440 0.9999 0.7160 0.9999 0.6873 0.9999 0.6581 0.9998 0.6285 0.9997

0.8472 1.0000 0.8259 1.0000 0.8033 1.0000 0.7796 0.9999 0.7548 0.9999

0.9161

0 10 0 10 20 0 10 20 0 10 20 0 10 20

0.0009 0.9015 0.0007 0.8867 1.0000 0.0006 0.8707 1.0000 0.0005 0.8535 1.0000 0.0004 0.8352 0.9999

0.0073 0.9467 0.0061 0.9371

0.0296 0.9730 0.0255 0.9673

0.0818 0.9872 0.0719 0.9841

0.1730 0.9943 0.1555 0.9927

0.3007 0.9976 0.2759 0.9969

0.4497 0.9990 0.4204 0.9987

0.5987 0.9996 0.5689 0.9995

0.7291 0.9999 0.7027 0.9998

0.8305 1.0000 0.8096 0.9999

0.0051 0.9265

0.0219 0.9609

0.0632 0.9805

0.1395 0.9908

0.2526 0.9959

0.3920 0.9983

0.5393 0.9993

0.6757 0.9997

0.7877 0.9999

0.0043 0.9148

0.0188 0.9536

0.0554 0.9762

0.1249 0.9886

0.2307 0.9948

0.3646 0.9978

0.5100 0.9991

0.6482 0.9996

0.7649 0.9999

0.0036 0.9020 1.0000

0.0161 0.9454

0.0485 0.9714

0.1117 0.9859

0.2103 0.9934

0.3384 0.9971

0.4812 0.9988

0.6204 0.9995

0.7411 0.9998

0 10 20 0 10 20 0 10 20 0 10 20 0 10 20

0.0003 0.8159 0.9999 0.0003 0.7955 0.9999 0.0002 0.7743 0.9998 0.0002 0.7522 0.9998 0.0002 0.7294 0.9997

0.0030 0.8881 1.0000 0.0025 0.8731 1.0000 0.0021 0.8571 0.9999 0.0018 0.8400 0.9999 0.0015 0.8220 0.9999

0.0138 0.9362

0.0424 0.9658

0.0996 0.9827

0.1912 0.9918

0.3134 0.9963

0.4530 0.9984

0.5925 0.9993

0.7166 0.9997

0.0118 0.9261

0.0370 0.9595

0.0887 0.9791

0.1736 0.9898

0.2896 0.9953

0.4254 0.9979

0.5647 0.9991

0.6915 0.9997

0.0100 0.9150 1.0000 0.0086 0.9029 1.0000 0.0073 0.8898 1.0000

0.0323 0.9524

0.0789 0.9749

0.1573 0.9875

0.2670 0.9941

0.3987 0.9973

0.5369 0.9989

0.6659 0.9995

0.0281 0.9445

0.0701 0.9701

0.1422 0.9848

0.2457 0.9926

0.3728 0.9966

0.5094 0.9985

0.6400 0.9994

0.0244 0.9358

0.0621 0.9647

0.1284 0.9816

0.2256 0.9909

0.3478 0.9957

0.4823 0.9981

0.6137 0.9992

0 10 20 0 10 20 0 10 20 0 10 20 0 10 20

0.0001 0.7060 0.9996 0.0001 0.6820 0.9994 0.0001 0.6576 0.9992 0.0001 0.6329 0.9990 0.0001 0.6080 0.9987

0.0012 0.8030 0.9998 0.0010 0.7832 0.9998 0.0009 0.7626 0.9997 0.0007 0.7412 0.9996 0.0006 0.7193 0.9995

0.0062 0.8758 0.9999 0.0053 0.8607 0.9999 0.0045 0.8448 0.9999 0.0038 0.8279 0.9998 0.0033 0.8101 0.9998

0.0212 0.9261 1.0000 0.0184 0.9156 1.0000 0.0160 0.9042 1.0000 0.0138 0.8919 0.9999 0.0120 0.8786 0.9999

0.0550 0.9585

0.1157 0.9780

0.2068 0.9889

0.3239 0.9947

0.4557 0.9976

0.5874 0.9989

0.0486 0.9517

0.1041 0.9738

0.1892 0.9865

0.3010 0.9934

0.4296 0.9969

0.5611 0.9986

0.0429 0.9441

0.0935 0.9691

0.1727 0.9838

0.2792 0.9919

0.4042 0.9962

0.5349 0.9983

0.0378 0.9357 1.0000 0.0333 0.9265 1.0000

0.0838 0.9638

0.1574 0.9806

0.2584 0.9902

0.3796 0.9952

0.5089 0.9978

0.0750 0.9579

0.1433 0.9770

0.2388 0.9881

0.3558 0.9941

0.4832 0.9972

0 10 20 0 10 20 0 10 20 0 10 20

0.0000 0.5830 0.9984 0.0000 0.5207 0.9972 0.0000 0.4599 0.9953 0.0000 0.4017 0.9925

0.0005 0.6968 0.9993 0.0003 0.6387 0.9987 0.0002 0.5793 0.9977 0.0001 0.5198 0.9962

0.0028 0.7916 0.9997 0.0018 0.7420 0.9994 0.0012 0.6887 0.9990 0.0008 0.6329 0.9982

0.0103 0.8645 0.9999 0.0071 0.8253 0.9998 0.0049 0.7813 0.9995 0.0034 0.7330 0.9992

0.0293 0.9165 1.0000 0.0211 0.8879 0.9999 0.0151 0.8540 0.9998 0.0107 0.8153 0.9996

0.0671 0.9513

0.1301 0.9730

0.2202 0.9857

0.3328 0.9928

0.4579 0.9965

0.0504 0.9317 1.0000 0.0375 0.9074 0.9999 0.0277 0.8783 0.9998

0.1016 0.9604

0.1785 0.9781

0.2794 0.9885

0.3971 0.9942

0.0786 0.9441 1.0000 0.0603 0.9236 0.9999

0.1432 0.9678

0.2320 0.9823

0.3405 0.9907

0.1137 0.9542 1.0000

0.1906 0.9738

0.2888 0.9857

0 10 20 0 10 20 0 10 20 0 10 20 30

0.0000 0.3472 0.9884 0.0000 0.2971 0.9827 0.0000 0.2517 0.9750 0.0000 0.2112 0.9649 1.0000

0.0001 0.4616 0.9939 0.0001 0.4058 0.9906 0.0000 0.3532 0.9859 0.0000 0.3045 0.9796

0.0005 0.5760 0.9970 0.0003 0.5190 0.9951 0.0002 0.4631 0.9924 0.0001 0.4093 0.9885

0.0023 0.6815 0.9985 0.0016 0.6278 0.9975 0.0011 0.5730 0.9960 0.0007 0.5182 0.9938

0.0076 0.7720 0.9993 0.0053 0.7250 0.9988 0.0037 0.6751 0.9980 0.0026 0.6233 0.9968

0.0203 0.8444 0.9997 0.0148 0.8060 0.9994 0.0107 0.7636 0.9990 0.0077 0.7178 0.9984

0.0458 0.8987 0.9999 0.0346 0.8693 0.9997 0.0259 0.8355 0.9995 0.0193 0.7975 0.9992

0.0895 0.9370 0.9999 0.0698 0.9158 0.9999 0.0540 0.8905 0.9998 0.0415 0.8609 0.9996

0.1550 0.9626 1.0000 0.1249 0.9481 1.0000 0.0998 0.9302 0.9999 0.0790 0.9084 0.9998

0.2424 0.9787

6.20 6.40 6.60 6.80

7.00 7.20

7.40

7.60

7.80

8.00

8.20

8.40

8.60

8.80

9.00

9.20

9.40

9.60

9.80

10.00

10.50

11.00

11.50

12.00

12.50

13.00

13.50

5

0.9016 0.8858 0.8686 1.0000 0.8502 1.0000

0.2014 0.9694 0.1658 0.9573 1.0000 0.1353 0.9421 0.9999

λ

x

0

1

2

3

4

5

6

7

8

9

14.00

0 10 20 30 0 10 20 30 0 10 20 30

0.0000 0.1757 0.9521 0.9999 0.0000 0.1449 0.9362 0.9999 0.0000 0.1185 0.9170 0.9998

0.0000 0.2600 0.9712 1.0000 0.0000 0.2201 0.9604 1.0000 0.0000 0.1848 0.9469 0.9999

0.0001 0.3585 0.9833

0.0005 0.4644 0.9907

0.0018 0.5704 0.9950

0.0055 0.6694 0.9974

0.0142 0.7559 0.9987

0.0316 0.8272 0.9994

0.0621 0.8826 0.9997

0.1094 0.9235 0.9999

0.0001 0.3111 0.9763

0.0003 0.4125 0.9863

0.0012 0.5176 0.9924

0.0039 0.6192 0.9959

0.0105 0.7112 0.9979

0.0239 0.7897 0.9989

0.0484 0.8530 0.9995

0.0878 0.9012 0.9998

0.0000 0.2676 0.9673 1.0000

0.0002 0.3632 0.9805

0.0009 0.4657 0.9888

0.0028 0.5681 0.9938

0.0076 0.6641 0.9967

0.0180 0.7489 0.9983

0.0374 0.8195 0.9991

0.0699 0.8752 0.9996

0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30

0.0000 0.0774 0.8682 0.9994 0.0000 0.0491 0.8055 0.9986 0.0000 0.0304 0.7307 0.9967 0.0000 0.0183 0.6472 0.9930

0.0000 0.1270 0.9108 0.9997 0.0000 0.0847 0.8615 0.9993 0.0000 0.0549 0.7991 0.9982 0.0000 0.0347 0.7255 0.9960

0.0000 0.1931 0.9418 0.9999 0.0000 0.1350 0.9047 0.9996 0.0000 0.0917 0.8551 0.9990 0.0000 0.0606 0.7931 0.9978

0.0001 0.2745 0.9633 0.9999 0.0000 0.2009 0.9367 0.9998 0.0000 0.1426 0.8989 0.9995 0.0000 0.0984 0.8490 0.9988

0.0004 0.3675 0.9777 1.0000 0.0002 0.2808 0.9594 0.9999 0.0001 0.2081 0.9317 0.9998 0.0000 0.1497 0.8933 0.9994

0.0014 0.4667 0.9869

0.0040 0.5660 0.9925

0.0100 0.6593 0.9959

0.0220 0.7423 0.9978

0.0433 0.8122 0.9989

0.0007 0.3715 0.9748 1.0000 0.0003 0.2867 0.9554 0.9999 0.0002 0.2148 0.9269 0.9997

0.0021 0.4677 0.9848

0.0054 0.5640 0.9912

0.0126 0.6550 0.9950

0.0261 0.7363 0.9973

0.0010 0.3751 0.9718 0.9999 0.0005 0.2920 0.9514 0.9998

0.0029 0.4686 0.9827 1.0000 0.0015 0.3784 0.9687 0.9999

0.0071 0.5622 0.9897

0.0154 0.6509 0.9941

0.0039 0.4695 0.9805 1.0000

0.0089 0.5606 0.9882

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0.0000 0.0108 0.5591 0.9865 1.0000 0.0000 0.0063 0.4710 0.9758 0.9999 0.0000 0.0035 0.3869 0.9595 0.9998

0.0000 0.0214 0.6437 0.9919

0.0000 0.0390 0.7206 0.9953

0.0000 0.0661 0.7875 0.9973

0.0000 0.1049 0.8432 0.9985

0.0001 0.1565 0.8878 0.9992

0.0003 0.2211 0.9221 0.9996

0.0008 0.2970 0.9475 0.9998

0.0021 0.3814 0.9657 0.9999

0.0050 0.4703 0.9782 0.9999

0.0000 0.0129 0.5577 0.9848 1.0000 0.0000 0.0076 0.4716 0.9735 0.9999

0.0000 0.0245 0.6405 0.9907

0.0000 0.0434 0.7160 0.9945

0.0000 0.0716 0.7822 0.9968

0.0000 0.1111 0.8377 0.9982

0.0001 0.1629 0.8826 0.9990

0.0004 0.2270 0.9175 0.9995

0.0011 0.3017 0.9436 0.9997

0.0028 0.3843 0.9626 0.9999

0.0000 0.0151 0.5564 0.9831 1.0000

0.0000 0.0278 0.6374 0.9895

0.0000 0.0477 0.7117 0.9936

0.0000 0.0769 0.7771 0.9962

0.0001 0.1170 0.8324 0.9978

0.0002 0.1690 0.8775 0.9988

0.0006 0.2325 0.9129 0.9993

0.0015 0.3060 0.9398 0.9996

0 10 20 30 40 0 10 20 30 40 0 10 20 30 40

0.0000 0.0020 0.3101 0.9360 0.9996 0.0000 0.0011 0.2426 0.9042 0.9990 0.0000 0.0006 0.1855 0.8633 0.9980

0.0000 0.0044 0.3894 0.9564 0.9998 0.0000 0.0025 0.3139 0.9322 0.9995 0.0000 0.0014 0.2473 0.8999 0.9988

0.0000 0.0091 0.4723 0.9711 0.9999 0.0000 0.0054 0.3917 0.9533 0.9997 0.0000 0.0031 0.3175 0.9285 0.9993

0.0000 0.0174 0.5551 0.9813 0.9999 0.0000 0.0107 0.4728 0.9686 0.9998 0.0000 0.0065 0.3939 0.9502 0.9996

0.0000 0.0311 0.6346 0.9882 1.0000 0.0000 0.0198 0.5540 0.9794 0.9999 0.0000 0.0124 0.4734 0.9662 0.9998

0.0000 0.0520 0.7077 0.9927

0.0000 0.0821 0.7723 0.9956

0.0001 0.1228 0.8274 0.9974

0.0003 0.1748 0.8726 0.9985

0.0008 0.2377 0.9085 0.9992

0.0000 0.0344 0.6319 0.9868 1.0000 0.0000 0.0223 0.5529 0.9775 0.9999

0.0000 0.0563 0.7038 0.9918

0.0000 0.0871 0.7677 0.9950

0.0002 0.1283 0.8225 0.9970

0.0004 0.1803 0.8679 0.9983

0.0000 0.0377 0.6294 0.9854 0.9999

0.0000 0.0605 0.7002 0.9908 1.0000

0.0001 0.0920 0.7634 0.9943

0.0002 0.1336 0.8179 0.9966

0 10 20 30 40 50 0 10 20 30 40 50 60

0.0000 0.0000 0.0353 0.5484 0.9677 0.9997 0.0000 0.0000 0.0043 0.2269 0.8249 0.9935 1.0000

0.0000 0.0001 0.0544 0.6186 0.9779 0.9998 0.0000 0.0000 0.0076 0.2833 0.8631 0.9957

0.0000 0.0002 0.0806 0.6845 0.9852 0.9999 0.0000 0.0000 0.0128 0.3449 0.8950 0.9973

0.0000 0.0004 0.1146 0.7444 0.9903 0.9999 0.0000 0.0000 0.0208 0.4102 0.9209 0.9983

0.0000 0.0009 0.1572 0.7973 0.9937 1.0000 0.0000 0.0000 0.0324 0.4775 0.9415 0.9989

0.0000 0.0019 0.2084 0.8426 0.9960

0.0000 0.0039 0.2673 0.8804 0.9975

0.0000 0.0073 0.3329 0.9110 0.9985

0.0000 0.0129 0.4031 0.9352 0.9991

0.0000 0.0219 0.4757 0.9537 0.9995

0.0000 0.0001 0.0486 0.5448 0.9575 0.9993

0.0000 0.0003 0.0705 0.6102 0.9697 0.9996

0.0000 0.0006 0.0988 0.6721 0.9788 0.9998

0.0000 0.0012 0.1343 0.7291 0.9854 0.9999

0.0000 0.0023 0.1770 0.7802 0.9902 0.9999

0 10 20 30 40 50 60

0.0000 0.0000 0.0004 0.0617 0.5419 0.9474 0.9988

0.0000 0.0000 0.0007 0.0855 0.6033 0.9613 0.9992

0.0000 0.0000 0.0014 0.1153 0.6618 0.9719 0.9995

0.0000 0.0000 0.0026 0.1514 0.7162 0.9800 0.9997

0.0000 0.0000 0.0045 0.1939 0.7657 0.9860 0.9998

0.0000 0.0000 0.0076 0.2424 0.8097 0.9903 0.9999

0.0000 0.0000 0.0123 0.2963 0.8479 0.9934 0.9999

0.0000 0.0000 0.0193 0.3547 0.8804 0.9956 1.0000

0.0000 0.0001 0.0294 0.4160 0.9075 0.9971

0.0000 0.0002 0.0432 0.4790 0.9297 0.9981

14.50

15.00

16.00

17.00

18.00

19.00

20.00

21.00

22.00

23.00

24.00

25.00

30.00

35.00

40.00

6

Tabela 3: Fun¸ca˜o de distribui¸c˜ao Normal reduzida: Z ∼ N (0, 1)

Z

z

Φ(z) = −∞

√

1 2 1 e− 2 t dt 2π 0

z

z

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.0 0.1 0.2 0.3 0.4

0.5000 0.5398 0.5793 0.6179 0.6554

0.5040 0.5438 0.5832 0.6217 0.6591

0.5080 0.5478 0.5871 0.6255 0.6628

0.5120 0.5517 0.5910 0.6293 0.6664

0.5160 0.5557 0.5948 0.6331 0.6700

0.5199 0.5596 0.5987 0.6368 0.6736

0.5239 0.5636 0.6026 0.6406 0.6772

0.5279 0.5675 0.6064 0.6443 0.6808

0.5319 0.5714 0.6103 0.6480 0.6844

0.5359 0.5753 0.6141 0.6517 0.6879

0.5 0.6 0.7 0.8 0.9

0.6915 0.7257 0.7580 0.7881 0.8159

0.6950 0.7291 0.7611 0.7910 0.8186

0.6985 0.7324 0.7642 0.7939 0.8212

0.7019 0.7357 0.7673 0.7967 0.8238

0.7054 0.7389 0.7704 0.7995 0.8264

0.7088 0.7422 0.7734 0.8023 0.8289

0.7123 0.7454 0.7764 0.8051 0.8315

0.7157 0.7486 0.7794 0.8078 0.8340

0.7190 0.7517 0.7823 0.8106 0.8365

0.7224 0.7549 0.7852 0.8133 0.8389

1.0 1.1 1.2 1.3 1.4

0.8413 0.8643 0.8849 0.9032 0.9192

0.8438 0.8665 0.8869 0.9049 0.9207

0.8461 0.8686 0.8888 0.9066 0.9222

0.8485 0.8708 0.8907 0.9082 0.9236

0.8508 0.8729 0.8925 0.9099 0.9251

0.8531 0.8749 0.8944 0.9115 0.9265

0.8554 0.8770 0.8962 0.9131 0.9279

0.8577 0.8790 0.8980 0.9147 0.9292

0.8599 0.8810 0.8997 0.9162 0.9306

0.8621 0.8830 0.9015 0.9177 0.9319

1.5 1.6 1.7 1.8 1.9

0.9332 0.9452 0.9554 0.9641 0.9713

0.9345 0.9463 0.9564 0.9649 0.9719

0.9357 0.9474 0.9573 0.9656 0.9726

0.9370 0.9484 0.9582 0.9664 0.9732

0.9382 0.9495 0.9591 0.9671 0.9738

0.9394 0.9505 0.9599 0.9678 0.9744

0.9406 0.9515 0.9608 0.9686 0.9750

0.9418 0.9525 0.9616 0.9693 0.9756

0.9429 0.9535 0.9625 0.9699 0.9761

0.9441 0.9545 0.9633 0.9706 0.9767

2.0 2.1 2.2 2.3 2.4

0.9772 0.9821 0.9861 0.9893 0.9918

0.9778 0.9826 0.9864 0.9896 0.9920

0.9783 0.9830 0.9868 0.9898 0.9922

0.9788 0.9834 0.9871 0.9901 0.9925

0.9793 0.9838 0.9875 0.9904 0.9927

0.9798 0.9842 0.9878 0.9906 0.9929

0.9803 0.9846 0.9881 0.9909 0.9931

0.9808 0.9850 0.9884 0.9911 0.9932

0.9812 0.9854 0.9887 0.9913 0.9934

0.9817 0.9857 0.9890 0.9916 0.9936

2.5 2.6 2.7 2.8 2.9

0.9938 0.9953 0.9965 0.9974 0.9981

0.9940 0.9955 0.9966 0.9975 0.9982

0.9941 0.9956 0.9967 0.9976 0.9982

0.9943 0.9957 0.9968 0.9977 0.9983

0.9945 0.9959 0.9969 0.9977 0.9984

0.9946 0.9960 0.9970 0.9978 0.9984

0.9948 0.9961 0.9971 0.9979 0.9985

0.9949 0.9962 0.9972 0.9979 0.9985

0.9951 0.9963 0.9973 0.9980 0.9986

0.9952 0.9964 0.9974 0.9981 0.9986

3.0 3.1 3.2 3.3 3.4

0.998650 0.999032 0.999313 0.999517 0.999663

0.998694 0.999064 0.999336 0.999533 0.999675

0.998736 0.999096 0.999359 0.999550 0.999687

0.998777 0.999126 0.999381 0.999566 0.999698

0.998817 0.999155 0.999402 0.999581 0.999709

0.998856 0.999184 0.999423 0.999596 0.999720

0.998893 0.999211 0.999443 0.999610 0.999730

0.998930 0.999238 0.999462 0.999624 0.999740

0.998965 0.999264 0.999481 0.999638 0.999749

0.998999 0.999289 0.999499 0.999650 0.999758

3.5 3.6 3.7 3.8 3.9 4.0

0.999767 0.999841 0.999892 0.999928 0.999952 0.999968

0.999776 0.999847 0.999896 0.999930 0.999954 0.999970

0.999784 0.999853 0.999900 0.999933 0.999956 0.999971

0.999792 0.999858 0.999904 0.999936 0.999958 0.999972

0.999800 0.999864 0.999908 0.999938 0.999959 0.999973

0.999807 0.999869 0.999912 0.999941 0.999961 0.999974

0.999815 0.999874 0.999915 0.999943 0.999963 0.999975

0.999821 0.999879 0.999918 0.999946 0.999964 0.999976

0.999828 0.999883 0.999922 0.999948 0.999966 0.999977

0.999835 0.999888 0.999925 0.999950 0.999967 0.999978

7

Tabela 4: Quantis da fun¸ca˜o de distribui¸c˜ao Z ∼ N (0, 1)

zp = Φ−1 (p) = Φ−1 (1 − q)

p q 0

zp

q

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

∞ 2.3263 2.0537 1.8808 1.7507 1.6449 1.5548 1.4758 1.4051 1.3408

3.0902 2.2904 2.0335 1.8663 1.7392 1.6352 1.5464 1.4684 1.3984 1.3346

2.8782 2.2571 2.0141 1.8522 1.7279 1.6258 1.5382 1.4611 1.3917 1.3285

2.7478 2.2262 1.9954 1.8384 1.7169 1.6164 1.5301 1.4538 1.3852 1.3225

2.6521 2.1973 1.9774 1.8250 1.7060 1.6072 1.5220 1.4466 1.3787 1.3165

2.5758 2.1701 1.9600 1.8119 1.6954 1.5982 1.5141 1.4395 1.3722 1.3106

2.5121 2.1444 1.9431 1.7991 1.6849 1.5893 1.5063 1.4325 1.3658 1.3047

2.4573 2.1201 1.9268 1.7866 1.6747 1.5805 1.4985 1.4255 1.3595 1.2988

2.4089 2.0969 1.9110 1.7744 1.6646 1.5718 1.4909 1.4187 1.3532 1.2930

2.3656 2.0748 1.8957 1.7624 1.6546 1.5632 1.4833 1.4118 1.3469 1.2873

2.3263 2.0537 1.8808 1.7507 1.6449 1.5548 1.4758 1.4051 1.3408 1.2816

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0.90

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19

1.2816 1.2265 1.1750 1.1264 1.0803 1.0364 0.9945 0.9542 0.9154 0.8779

1.2759 1.2212 1.1700 1.1217 1.0758 1.0322 0.9904 0.9502 0.9116 0.8742

1.2702 1.2160 1.1650 1.1170 1.0714 1.0279 0.9863 0.9463 0.9078 0.8706

1.2646 1.2107 1.1601 1.1123 1.0669 1.0237 0.9822 0.9424 0.9040 0.8669

1.2591 1.2055 1.1552 1.1077 1.0625 1.0194 0.9782 0.9385 0.9002 0.8632

1.2536 1.2004 1.1503 1.1031 1.0581 1.0152 0.9741 0.9346 0.8965 0.8596

1.2481 1.1952 1.1455 1.0985 1.0537 1.0110 0.9701 0.9307 0.8927 0.8560

1.2426 1.1901 1.1407 1.0939 1.0494 1.0069 0.9661 0.9269 0.8890 0.8524

1.2372 1.1850 1.1359 1.0893 1.0451 1.0027 0.9621 0.9230 0.8853 0.8488

1.2319 1.1800 1.1311 1.0848 1.0407 0.9986 0.9581 0.9192 0.8816 0.8452

1.2265 1.1750 1.1264 1.0803 1.0364 0.9945 0.9542 0.9154 0.8779 0.8416

0.89 0.88 0.87 0.86 0.85 0.84 0.83 0.82 0.81 0.80

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

0.8416 0.8064 0.7722 0.7388 0.7063 0.6745 0.6433 0.6128 0.5828 0.5534

0.8381 0.8030 0.7688 0.7356 0.7031 0.6713 0.6403 0.6098 0.5799 0.5505

0.8345 0.7995 0.7655 0.7323 0.6999 0.6682 0.6372 0.6068 0.5769 0.5476

0.8310 0.7961 0.7621 0.7290 0.6967 0.6651 0.6341 0.6038 0.5740 0.5446

0.8274 0.7926 0.7588 0.7257 0.6935 0.6620 0.6311 0.6008 0.5710 0.5417

0.8239 0.7892 0.7554 0.7225 0.6903 0.6588 0.6280 0.5978 0.5681 0.5388

0.8204 0.7858 0.7521 0.7192 0.6871 0.6557 0.6250 0.5948 0.5651 0.5359

0.8169 0.7824 0.7488 0.7160 0.6840 0.6526 0.6219 0.5918 0.5622 0.5330

0.8134 0.7790 0.7454 0.7128 0.6808 0.6495 0.6189 0.5888 0.5592 0.5302

0.8099 0.7756 0.7421 0.7095 0.6776 0.6464 0.6158 0.5858 0.5563 0.5273

0.8064 0.7722 0.7388 0.7063 0.6745 0.6433 0.6128 0.5828 0.5534 0.5244

0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.72 0.71 0.70

0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

0.5244 0.4958 0.4677 0.4399 0.4125 0.3853 0.3585 0.3319 0.3055 0.2793

0.5215 0.4930 0.4649 0.4372 0.4097 0.3826 0.3558 0.3292 0.3029 0.2767

0.5187 0.4902 0.4621 0.4344 0.4070 0.3799 0.3531 0.3266 0.3002 0.2741

0.5158 0.4874 0.4593 0.4316 0.4043 0.3772 0.3505 0.3239 0.2976 0.2715

0.5129 0.4845 0.4565 0.4289 0.4016 0.3745 0.3478 0.3213 0.2950 0.2689

0.5101 0.4817 0.4538 0.4261 0.3989 0.3719 0.3451 0.3186 0.2924 0.2663

0.5072 0.4789 0.4510 0.4234 0.3961 0.3692 0.3425 0.3160 0.2898 0.2637

0.5044 0.4761 0.4482 0.4207 0.3934 0.3665 0.3398 0.3134 0.2871 0.2611

0.5015 0.4733 0.4454 0.4179 0.3907 0.3638 0.3372 0.3107 0.2845 0.2585

0.4987 0.4705 0.4427 0.4152 0.3880 0.3611 0.3345 0.3081 0.2819 0.2559

0.4958 0.4677 0.4399 0.4125 0.3853 0.3585 0.3319 0.3055 0.2793 0.2533

0.69 0.68 0.67 0.66 0.65 0.64 0.63 0.62 0.61 0.60

0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49

0.2533 0.2275 0.2019 0.1764 0.1510 0.1257 0.1004 0.0753 0.0502 0.0251

0.2508 0.2250 0.1993 0.1738 0.1484 0.1231 0.0979 0.0728 0.0476 0.0226

0.2482 0.2224 0.1968 0.1713 0.1459 0.1206 0.0954 0.0702 0.0451 0.0201

0.2456 0.2198 0.1942 0.1687 0.1434 0.1181 0.0929 0.0677 0.0426 0.0175

0.2430 0.2173 0.1917 0.1662 0.1408 0.1156 0.0904 0.0652 0.0401 0.0150

0.2404 0.2147 0.1891 0.1637 0.1383 0.1130 0.0878 0.0627 0.0376 0.0125

0.2378 0.2121 0.1866 0.1611 0.1358 0.1105 0.0853 0.0602 0.0351 0.0100

0.2353 0.2096 0.1840 0.1586 0.1332 0.1080 0.0828 0.0577 0.0326 0.0075

0.2327 0.2070 0.1815 0.1560 0.1307 0.1055 0.0803 0.0552 0.0301 0.0050

0.2301 0.2045 0.1789 0.1535 0.1282 0.1030 0.0778 0.0527 0.0276 0.0025

0.2275 0.2019 0.1764 0.1510 0.1257 0.1004 0.0753 0.0502 0.0251 0.0000

0.59 0.58 0.57 0.56 0.55 0.54 0.53 0.52 0.51 0.50

0.010

0.009

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

0.000

p

8

Tabela 5: Quantis da fun¸ca˜o de distribui¸c˜ao t-Student X ∼ t(n) : xp = FX−1 (p)

p 0

xp

n\p

0.6

0.7

0.75

0.8

0.85

0.9

0.925

0.95

0.975

0.99

0.995

0.999

0.9995

1 2 3 4 5

0.325 0.289 0.277 0.271 0.267

0.727 0.617 0.584 0.569 0.559

1.000 0.816 0.765 0.741 0.727

1.376 1.061 0.978 0.941 0.920

1.963 1.386 1.250 1.190 1.156

3.078 1.886 1.638 1.533 1.476

4.165 2.282 1.924 1.778 1.699

6.314 2.920 2.353 2.132 2.015

12.706 4.303 3.182 2.776 2.571

31.821 6.965 4.541 3.747 3.365

63.656 9.925 5.841 4.604 4.032

318.289 22.328 10.214 7.173 5.894

636.578 31.600 12.924 8.610 6.869

6 7 8 9 10

0.265 0.263 0.262 0.261 0.260

0.553 0.549 0.546 0.543 0.542

0.718 0.711 0.706 0.703 0.700

0.906 0.896 0.889 0.883 0.879

1.134 1.119 1.108 1.100 1.093

1.440 1.415 1.397 1.383 1.372

1.650 1.617 1.592 1.574 1.559

1.943 1.895 1.860 1.833 1.812

2.447 2.365 2.306 2.262 2.228

3.143 2.998 2.896 2.821 2.764

3.707 3.499 3.355 3.250 3.169

5.208 4.785 4.501 4.297 4.144

5.959 5.408 5.041 4.781 4.587

11 12 13 14 15

0.260 0.259 0.259 0.258 0.258

0.540 0.539 0.538 0.537 0.536

0.697 0.695 0.694 0.692 0.691

0.876 0.873 0.870 0.868 0.866

1.088 1.083 1.079 1.076 1.074

1.363 1.356 1.350 1.345 1.341

1.548 1.538 1.530 1.523 1.517

1.796 1.782 1.771 1.761 1.753

2.201 2.179 2.160 2.145 2.131

2.718 2.681 2.650 2.624 2.602

3.106 3.055 3.012 2.977 2.947

4.025 3.930 3.852 3.787 3.733

4.437 4.318 4.221 4.140 4.073

16 17 18 19 20

0.258 0.257 0.257 0.257 0.257

0.535 0.534 0.534 0.533 0.533

0.690 0.689 0.688 0.688 0.687

0.865 0.863 0.862 0.861 0.860

1.071 1.069 1.067 1.066 1.064

1.337 1.333 1.330 1.328 1.325

1.512 1.508 1.504 1.500 1.497

1.746 1.740 1.734 1.729 1.725

2.120 2.110 2.101 2.093 2.086

2.583 2.567 2.552 2.539 2.528

2.921 2.898 2.878 2.861 2.845

3.686 3.646 3.610 3.579 3.552

4.015 3.965 3.922 3.883 3.850

21 22 23 24 25

0.257 0.256 0.256 0.256 0.256

0.532 0.532 0.532 0.531 0.531

0.686 0.686 0.685 0.685 0.684

0.859 0.858 0.858 0.857 0.856

1.063 1.061 1.060 1.059 1.058

1.323 1.321 1.319 1.318 1.316

1.494 1.492 1.489 1.487 1.485

1.721 1.717 1.714 1.711 1.708

2.080 2.074 2.069 2.064 2.060

2.518 2.508 2.500 2.492 2.485

2.831 2.819 2.807 2.797 2.787

3.527 3.505 3.485 3.467 3.450

3.819 3.792 3.768 3.745 3.725

26 27 28 29 30

0.256 0.256 0.256 0.256 0.256

0.531 0.531 0.530 0.530 0.530

0.684 0.684 0.683 0.683 0.683

0.856 0.855 0.855 0.854 0.854

1.058 1.057 1.056 1.055 1.055

1.315 1.314 1.313 1.311 1.310

1.483 1.482 1.480 1.479 1.477

1.706 1.703 1.701 1.699 1.697

2.056 2.052 2.048 2.045 2.042

2.479 2.473 2.467 2.462 2.457

2.779 2.771 2.763 2.756 2.750

3.435 3.421 3.408 3.396 3.385

3.707 3.689 3.674 3.660 3.646

40 45 50 60 70

0.255 0.255 0.255 0.254 0.254

0.529 0.528 0.528 0.527 0.527

0.681 0.680 0.679 0.679 0.678

0.851 0.850 0.849 0.848 0.847

1.050 1.049 1.047 1.045 1.044

1.303 1.301 1.299 1.296 1.294

1.468 1.465 1.462 1.458 1.456

1.684 1.679 1.676 1.671 1.667

2.021 2.014 2.009 2.000 1.994

2.423 2.412 2.403 2.390 2.381

2.704 2.690 2.678 2.660 2.648

3.307 3.281 3.261 3.232 3.211

3.551 3.520 3.496 3.460 3.435

80 90 100 120 150

0.254 0.254 0.254 0.254 0.254

0.526 0.526 0.526 0.526 0.526

0.678 0.677 0.677 0.677 0.676

0.846 0.846 0.845 0.845 0.844

1.043 1.042 1.042 1.041 1.040

1.292 1.291 1.290 1.289 1.287

1.453 1.452 1.451 1.449 1.447

1.664 1.662 1.660 1.658 1.655

1.990 1.987 1.984 1.980 1.976

2.374 2.368 2.364 2.358 2.351

2.639 2.632 2.626 2.617 2.609

3.195 3.183 3.174 3.160 3.145

3.416 3.402 3.390 3.373 3.357

∞

0.253

0.524

0.675

0.842

1.036

1.282

1.440

1.645

1.960

2.327

2.576

3.091

3.291

9

0.0005

3.9E-07 0.0010 0.0153 0.0639 0.158 0.299 0.485 0.710 0.972 1.265 1.587 1.935 2.305 2.697 3.107 3.536 3.980 4.439 4.913 5.398 5.895 6.404 6.924 7.453 7.991 8.537 9.093 9.656 10.23 10.80 11.39 11.98 12.58 13.18 13.79 14.40 15.02 15.64 16.27 16.91 23.46 30.34 37.47 44.79 52.28 59.89 75.47 99.46 140.7

n\p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 50 60 70 80 90 100 120 150 200

1.6E-06 0.0020 0.0243 0.0908 0.210 0.381 0.599 0.857 1.152 1.479 1.834 2.214 2.617 3.041 3.483 3.942 4.416 4.905 5.407 5.921 6.447 6.983 7.529 8.085 8.649 9.222 9.803 10.39 10.99 11.59 12.20 12.81 13.43 14.06 14.69 15.32 15.97 16.61 17.26 17.92 24.67 31.74 39.04 46.52 54.16 61.92 77.76 102.1 143.8

0.001

3.9E-05 0.0100 0.0717 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 4.601 5.142 5.697 6.265 6.844 7.434 8.034 8.643 9.260 9.886 10.52 11.16 11.81 12.46 13.12 13.79 14.46 15.13 15.82 16.50 17.19 17.89 18.59 19.29 20.00 20.71 27.99 35.53 43.28 51.17 59.20 67.33 83.85 109.1 152.2

0.005

0.0002 0.0201 0.115 0.297 0.554 0.872 1.239 1.647 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.20 10.86 11.52 12.20 12.88 13.56 14.26 14.95 15.66 16.36 17.07 17.79 18.51 19.23 19.96 20.69 21.43 22.16 29.71 37.48 45.44 53.54 61.75 70.06 86.92 112.7 156.4

0.01

0.0010 0.0506 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.28 10.98 11.69 12.40 13.12 13.84 14.57 15.31 16.05 16.79 17.54 18.29 19.05 19.81 20.57 21.34 22.11 22.88 23.65 24.43 32.36 40.48 48.76 57.15 65.65 74.22 91.57 118.0 162.7

0.025

0.0039 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.12 10.85 11.59 12.34 13.09 13.85 14.61 15.38 16.15 16.93 17.71 18.49 19.28 20.07 20.87 21.66 22.47 23.27 24.07 24.88 25.70 26.51 34.76 43.19 51.74 60.39 69.13 77.93 95.70 122.7 168.3

0.05

0.0089 0.156 0.472 0.897 1.394 1.941 2.528 3.144 3.785 4.446 5.124 5.818 6.524 7.242 7.969 8.707 9.452 10.21 10.97 11.73 12.50 13.28 14.06 14.85 15.64 16.44 17.24 18.05 18.85 19.66 20.48 21.30 22.12 22.94 23.76 24.59 25.42 26.25 27.09 27.93 36.40 45.02 53.75 62.57 71.46 80.41 98.46 125.8 172.0

0.075

0.0158 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.041 7.790 8.547 9.312 10.09 10.86 11.65 12.44 13.24 14.04 14.85 15.66 16.47 17.29 18.11 18.94 19.77 20.60 21.43 22.27 23.11 23.95 24.80 25.64 26.49 27.34 28.20 29.05 37.69 46.46 55.33 64.28 73.29 82.36 100.6 128.3 174.8

0.10

0.0358 0.325 0.798 1.366 1.994 2.661 3.358 4.078 4.817 5.570 6.336 7.114 7.901 8.696 9.499 10.31 11.12 11.95 12.77 13.60 14.44 15.28 16.12 16.97 17.82 18.67 19.53 20.39 21.25 22.11 22.98 23.84 24.71 25.59 26.46 27.34 28.21 29.09 29.97 30.86 39.75 48.76 57.84 66.99 76.20 85.44 104.0 132.1 179.4

0.15

0.0642 0.446 1.005 1.649 2.343 3.070 3.822 4.594 5.380 6.179 6.989 7.807 8.634 9.467 10.31 11.15 12.00 12.86 13.72 14.58 15.44 16.31 17.19 18.06 18.94 19.82 20.70 21.59 22.48 23.36 24.26 25.15 26.04 26.94 27.84 28.73 29.64 30.54 31.44 32.34 41.45 50.64 59.90 69.21 78.56 87.95 106.8 135.3 183.0

0.20

0.148 0.713 1.424 2.195 3.000 3.828 4.671 5.527 6.393 7.267 8.148 9.034 9.926 10.82 11.72 12.62 13.53 14.44 15.35 16.27 17.18 18.10 19.02 19.94 20.87 21.79 22.72 23.65 24.58 25.51 26.44 27.37 28.31 29.24 30.18 31.12 32.05 32.99 33.93 34.87 44.31 53.81 63.35 72.92 82.51 92.13 111.4 140.5 189.0

0.30

0.275 1.022 1.869 2.753 3.656 4.570 5.493 6.423 7.357 8.295 9.237 10.18 11.13 12.08 13.03 13.98 14.94 15.89 16.85 17.81 18.77 19.73 20.69 21.65 22.62 23.58 24.54 25.51 26.48 27.44 28.41 29.38 30.34 31.31 32.28 33.25 34.22 35.19 36.16 37.13 46.86 56.62 66.40 76.19 85.99 95.81 115.5 145.0 194.3

0.40

0.455 1.386 2.366 3.357 4.351 5.348 6.346 7.344 8.343 9.342 10.34 11.34 12.34 13.34 14.34 15.34 16.34 17.34 18.34 19.34 20.34 21.34 22.34 23.34 24.34 25.34 26.34 27.34 28.34 29.34 30.34 31.34 32.34 33.34 34.34 35.34 36.34 37.34 38.34 39.34 49.33 59.33 69.33 79.33 89.33 99.33 119.3 149.3 199.3

0.50

0.708 1.833 2.946 4.045 5.132 6.211 7.283 8.351 9.414 10.47 11.53 12.58 13.64 14.69 15.73 16.78 17.82 18.87 19.91 20.95 21.99 23.03 24.07 25.11 26.14 27.18 28.21 29.25 30.28 31.32 32.35 33.38 34.41 35.44 36.47 37.50 38.53 39.56 40.59 41.62 51.89 62.13 72.36 82.57 92.76 102.9 123.3 153.8 204.4

0.60

1.074 2.408 3.665 4.878 6.064 7.231 8.383 9.524 10.66 11.78 12.90 14.01 15.12 16.22 17.32 18.42 19.51 20.60 21.69 22.77 23.86 24.94 26.02 27.10 28.17 29.25 30.32 31.39 32.46 33.53 34.60 35.66 36.73 37.80 38.86 39.92 40.98 42.05 43.11 44.16 54.72 65.23 75.69 86.12 96.52 106.9 127.6 158.6 210.0

0.70

1.642 3.219 4.642 5.989 7.289 8.558 9.803 11.03 12.24 13.44 14.63 15.81 16.98 18.15 19.31 20.47 21.61 22.76 23.90 25.04 26.17 27.30 28.43 29.55 30.68 31.79 32.91 34.03 35.14 36.25 37.36 38.47 39.57 40.68 41.78 42.88 43.98 45.08 46.17 47.27 58.16 68.97 79.71 90.41 101.1 111.7 132.8 164.3 216.6

0.80

2.072 3.794 5.317 6.745 8.115 9.446 10.75 12.03 13.29 14.53 15.77 16.99 18.20 19.41 20.60 21.79 22.98 24.16 25.33 26.50 27.66 28.82 29.98 31.13 32.28 33.43 34.57 35.71 36.85 37.99 39.12 40.26 41.39 42.51 43.64 44.76 45.89 47.01 48.13 49.24 60.35 71.34 82.26 93.11 103.9 114.7 136.1 168.0 220.7

0.85

2.706 4.605 6.251 7.779 9.236 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26 41.42 42.58 43.75 44.90 46.06 47.21 48.36 49.51 50.66 51.81 63.17 74.40 85.53 96.58 107.6 118.5 140.2 172.6 226.0

0.90

3.170 5.181 6.905 8.496 10.01 11.47 12.88 14.27 15.63 16.97 18.29 19.60 20.90 22.18 23.45 24.72 25.97 27.22 28.46 29.69 30.92 32.14 33.36 34.57 35.78 36.98 38.18 39.38 40.57 41.76 42.95 44.13 45.31 46.49 47.66 48.84 50.01 51.17 52.34 53.50 65.03 76.41 87.68 98.86 110.0 121.0 143.0 175.6 229.5

0.925

3.841 5.991 7.815 9.488 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77 44.99 46.19 47.40 48.60 49.80 51.00 52.19 53.38 54.57 55.76 67.50 79.08 90.53 101.9 113.1 124.3 146.6 179.6 234.0

0.950

5.024 7.378 9.348 11.14 12.83 14.45 16.01 17.53 19.02 20.48 21.92 23.34 24.74 26.12 27.49 28.85 30.19 31.53 32.85 34.17 35.48 36.78 38.08 39.36 40.65 41.92 43.19 44.46 45.72 46.98 48.23 49.48 50.73 51.97 53.20 54.44 55.67 56.90 58.12 59.34 71.42 83.30 95.02 106.6 118.1 129.6 152.2 185.8 241.1

0.975

6.635 9.210 11.34 13.28 15.09 16.81 18.48 20.09 21.67 23.21 24.73 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89 52.19 53.49 54.78 56.06 57.34 58.62 59.89 61.16 62.43 63.69 76.15 88.38 100.4 112.3 124.1 135.8 159.0 193.2 249.4

0.990

7.879 10.60 12.84 14.86 16.75 18.55 20.28 21.95 23.59 25.19 26.76 28.30 29.82 31.32 32.80 34.27 35.72 37.16 38.58 40.00 41.40 42.80 44.18 45.56 46.93 48.29 49.65 50.99 52.34 53.67 55.00 56.33 57.65 58.96 60.27 61.58 62.88 64.18 65.48 66.77 79.49 91.95 104.2 116.3 128.3 140.2 163.6 198.4 255.3

0.995

10.83 13.82 16.27 18.47 20.51 22.46 24.32 26.12 27.88 29.59 31.26 32.91 34.53 36.12 37.70 39.25 40.79 42.31 43.82 45.31 46.80 48.27 49.73 51.18 52.62 54.05 55.48 56.89 58.30 59.70 61.10 62.49 63.87 65.25 66.62 67.98 69.35 70.70 72.06 73.40 86.66 99.61 112.3 124.8 137.2 149.4 173.6 209.3 267.5

0.999

12.12 15.20 17.73 20.00 22.11 24.10 26.02 27.87 29.67 31.42 33.14 34.82 36.48 38.11 39.72 41.31 42.88 44.43 45.97 47.50 49.01 50.51 52.00 53.48 54.95 56.41 57.86 59.30 60.73 62.16 63.58 64.99 66.40 67.80 69.20 70.59 71.97 73.35 74.72 76.10 89.56 102.7 115.6 128.3 140.8 153.2 177.6 213.6 272.4

0.9995

Tabela 6: Quantis da fun¸ca˜o de distribui¸c˜ao Qui-quadrado X ∼ χ2(n) : xp = FX−1 (p)

10