tablas de probabilidades · 2009. 2. 5. · tablas de probabilidades 3 tabla 1b. probabilidades...
TRANSCRIPT
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Tablas de Probabilidades
Ernesto Barrios Zamudio
José Ángel Garćıa Pérez
Febrero 2009Versión 0.90
Índice
1. Distribución Binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Distribución Poisson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Distribución Normal Estándar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4. Distribución Gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5. Distribución t de Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6. Distribución χ2 Ji-Cuadrada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7. Distribución F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8. Distribución del estad́ıstico d de Durbin-Watson . . . . . . . . . . . . . . . . . . . . . . . 20
9. Distribución del estad́ıstico U de Corridas (Wald-Wolfowitz) . . . . . . . . . . . . . . . 29
10.Distribución del estad́ıstico ρs de Spearman . . . . . . . . . . . . . . . . . . . . . . . . . 33
11.Distribución del estad́ıstico U de Mann-Whitney . . . . . . . . . . . . . . . . . . . . . . 34
12.Distribución del estad́ıstico D de Kolmogorov-Smirnov . . . . . . . . . . . . . . . . . . . 39
13.1050 Números Seudoaleatorios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Notas
El cálculo de las probabilidades y las gráficas fueron generadas utilizando el lenguaje estad́ıstico R. Eldocumento fue preparado con LATEX y el uso del paquete-R xtable.
Copia electrónica de este documento lo encuentra en:http://allman.rhon.itam.mx/∼ebarrios/TablasProbabilidad.pdf
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http://allman.rhon.itam.mx/~ebarrios/TablasProbabilidad.pdf�
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Tablas de Probabilidades 2
1. Distribución Binomial
X ∼ Binom(n, ϕ)
p = P (X ≤ x) =x∑
k=0
(n
k
)ϕk(1− ϕ)n−k = 1− α
0 x n
p α
Tabla 1A. Probabilidades acumuladas p de la distribución binomial (n = 5, 6, 7, 8, 9).
ϕx 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99
n = 5 0 0.951 0.774 0.590 0.328 0.237 0.168 0.078 0.031 0.010 0.002 0.001 0.000 0.000 0.000 0.0001 0.999 0.977 0.919 0.737 0.633 0.528 0.337 0.188 0.087 0.031 0.016 0.007 0.000 0.000 0.0002 1.000 0.999 0.991 0.942 0.896 0.837 0.683 0.500 0.317 0.163 0.104 0.058 0.009 0.001 0.0003 1.000 1.000 1.000 0.993 0.984 0.969 0.913 0.813 0.663 0.472 0.367 0.263 0.081 0.023 0.0014 1.000 1.000 1.000 1.000 0.999 0.998 0.990 0.969 0.922 0.832 0.763 0.672 0.410 0.226 0.0495 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 6 0 0.941 0.735 0.531 0.262 0.178 0.118 0.047 0.016 0.004 0.001 0.000 0.000 0.000 0.000 0.0001 0.999 0.967 0.886 0.655 0.534 0.420 0.233 0.109 0.041 0.011 0.005 0.002 0.000 0.000 0.0002 1.000 0.998 0.984 0.901 0.831 0.744 0.544 0.344 0.179 0.070 0.038 0.017 0.001 0.000 0.0003 1.000 1.000 0.999 0.983 0.962 0.930 0.821 0.656 0.456 0.256 0.169 0.099 0.016 0.002 0.0004 1.000 1.000 1.000 0.998 0.995 0.989 0.959 0.891 0.767 0.580 0.466 0.345 0.114 0.033 0.0015 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.984 0.953 0.882 0.822 0.738 0.469 0.265 0.0596 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 7 0 0.932 0.698 0.478 0.210 0.133 0.082 0.028 0.008 0.002 0.000 0.000 0.000 0.000 0.000 0.0001 0.998 0.956 0.850 0.577 0.445 0.329 0.159 0.063 0.019 0.004 0.001 0.000 0.000 0.000 0.0002 1.000 0.996 0.974 0.852 0.756 0.647 0.420 0.227 0.096 0.029 0.013 0.005 0.000 0.000 0.0003 1.000 1.000 0.997 0.967 0.929 0.874 0.710 0.500 0.290 0.126 0.071 0.033 0.003 0.000 0.0004 1.000 1.000 1.000 0.995 0.987 0.971 0.904 0.773 0.580 0.353 0.244 0.148 0.026 0.004 0.0005 1.000 1.000 1.000 1.000 0.999 0.996 0.981 0.938 0.841 0.671 0.555 0.423 0.150 0.044 0.0026 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.992 0.972 0.918 0.867 0.790 0.522 0.302 0.0687 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 8 0 0.923 0.663 0.430 0.168 0.100 0.058 0.017 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.0001 0.997 0.943 0.813 0.503 0.367 0.255 0.106 0.035 0.009 0.001 0.000 0.000 0.000 0.000 0.0002 1.000 0.994 0.962 0.797 0.679 0.552 0.315 0.145 0.050 0.011 0.004 0.001 0.000 0.000 0.0003 1.000 1.000 0.995 0.944 0.886 0.806 0.594 0.363 0.174 0.058 0.027 0.010 0.000 0.000 0.0004 1.000 1.000 1.000 0.990 0.973 0.942 0.826 0.637 0.406 0.194 0.114 0.056 0.005 0.000 0.0005 1.000 1.000 1.000 0.999 0.996 0.989 0.950 0.855 0.685 0.448 0.321 0.203 0.038 0.006 0.0006 1.000 1.000 1.000 1.000 1.000 0.999 0.991 0.965 0.894 0.745 0.633 0.497 0.187 0.057 0.0037 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.983 0.942 0.900 0.832 0.570 0.337 0.0778 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 9 0 0.914 0.630 0.387 0.134 0.075 0.040 0.010 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.997 0.929 0.775 0.436 0.300 0.196 0.071 0.020 0.004 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.992 0.947 0.738 0.601 0.463 0.232 0.090 0.025 0.004 0.001 0.000 0.000 0.000 0.0003 1.000 0.999 0.992 0.914 0.834 0.730 0.483 0.254 0.099 0.025 0.010 0.003 0.000 0.000 0.0004 1.000 1.000 0.999 0.980 0.951 0.901 0.733 0.500 0.267 0.099 0.049 0.020 0.001 0.000 0.0005 1.000 1.000 1.000 0.997 0.990 0.975 0.901 0.746 0.517 0.270 0.166 0.086 0.008 0.001 0.0006 1.000 1.000 1.000 1.000 0.999 0.996 0.975 0.910 0.768 0.537 0.399 0.262 0.053 0.008 0.0007 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.980 0.929 0.804 0.700 0.564 0.225 0.071 0.0038 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.990 0.960 0.925 0.866 0.613 0.370 0.0869 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 3
Tabla 1B. Probabilidades acumuladas p de la distribución binomial (n = 10, 11, 12, 13, 14).
ϕx 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99
n = 10 0 0.904 0.599 0.349 0.107 0.056 0.028 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.996 0.914 0.736 0.376 0.244 0.149 0.046 0.011 0.002 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.988 0.930 0.678 0.526 0.383 0.167 0.055 0.012 0.002 0.000 0.000 0.000 0.000 0.0003 1.000 0.999 0.987 0.879 0.776 0.650 0.382 0.172 0.055 0.011 0.004 0.001 0.000 0.000 0.0004 1.000 1.000 0.998 0.967 0.922 0.850 0.633 0.377 0.166 0.047 0.020 0.006 0.000 0.000 0.0005 1.000 1.000 1.000 0.994 0.980 0.953 0.834 0.623 0.367 0.150 0.078 0.033 0.002 0.000 0.0006 1.000 1.000 1.000 0.999 0.996 0.989 0.945 0.828 0.618 0.350 0.224 0.121 0.013 0.001 0.0007 1.000 1.000 1.000 1.000 1.000 0.998 0.988 0.945 0.833 0.617 0.474 0.322 0.070 0.012 0.0008 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.989 0.954 0.851 0.756 0.624 0.264 0.086 0.0049 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.972 0.944 0.893 0.651 0.401 0.096
10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 11 0 0.895 0.569 0.314 0.086 0.042 0.020 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.995 0.898 0.697 0.322 0.197 0.113 0.030 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.985 0.910 0.617 0.455 0.313 0.119 0.033 0.006 0.001 0.000 0.000 0.000 0.000 0.0003 1.000 0.998 0.981 0.839 0.713 0.570 0.296 0.113 0.029 0.004 0.001 0.000 0.000 0.000 0.0004 1.000 1.000 0.997 0.950 0.885 0.790 0.533 0.274 0.099 0.022 0.008 0.002 0.000 0.000 0.0005 1.000 1.000 1.000 0.988 0.966 0.922 0.753 0.500 0.247 0.078 0.034 0.012 0.000 0.000 0.0006 1.000 1.000 1.000 0.998 0.992 0.978 0.901 0.726 0.467 0.210 0.115 0.050 0.003 0.000 0.0007 1.000 1.000 1.000 1.000 0.999 0.996 0.971 0.887 0.704 0.430 0.287 0.161 0.019 0.002 0.0008 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.967 0.881 0.687 0.545 0.383 0.090 0.015 0.0009 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.970 0.887 0.803 0.678 0.303 0.102 0.005
10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.980 0.958 0.914 0.686 0.431 0.10511 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 12 0 0.886 0.540 0.282 0.069 0.032 0.014 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.994 0.882 0.659 0.275 0.158 0.085 0.020 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.980 0.889 0.558 0.391 0.253 0.083 0.019 0.003 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.998 0.974 0.795 0.649 0.493 0.225 0.073 0.015 0.002 0.000 0.000 0.000 0.000 0.0004 1.000 1.000 0.996 0.927 0.842 0.724 0.438 0.194 0.057 0.009 0.003 0.001 0.000 0.000 0.0005 1.000 1.000 0.999 0.981 0.946 0.882 0.665 0.387 0.158 0.039 0.014 0.004 0.000 0.000 0.0006 1.000 1.000 1.000 0.996 0.986 0.961 0.842 0.613 0.335 0.118 0.054 0.019 0.001 0.000 0.0007 1.000 1.000 1.000 0.999 0.997 0.991 0.943 0.806 0.562 0.276 0.158 0.073 0.004 0.000 0.0008 1.000 1.000 1.000 1.000 1.000 0.998 0.985 0.927 0.775 0.507 0.351 0.205 0.026 0.002 0.0009 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.981 0.917 0.747 0.609 0.442 0.111 0.020 0.000
10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.980 0.915 0.842 0.725 0.341 0.118 0.00611 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.986 0.968 0.931 0.718 0.460 0.11412 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 13 0 0.878 0.513 0.254 0.055 0.024 0.010 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.993 0.865 0.621 0.234 0.127 0.064 0.013 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.975 0.866 0.502 0.333 0.202 0.058 0.011 0.001 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.997 0.966 0.747 0.584 0.421 0.169 0.046 0.008 0.001 0.000 0.000 0.000 0.000 0.0004 1.000 1.000 0.994 0.901 0.794 0.654 0.353 0.133 0.032 0.004 0.001 0.000 0.000 0.000 0.0005 1.000 1.000 0.999 0.970 0.920 0.835 0.574 0.291 0.098 0.018 0.006 0.001 0.000 0.000 0.0006 1.000 1.000 1.000 0.993 0.976 0.938 0.771 0.500 0.229 0.062 0.024 0.007 0.000 0.000 0.0007 1.000 1.000 1.000 0.999 0.994 0.982 0.902 0.709 0.426 0.165 0.080 0.030 0.001 0.000 0.0008 1.000 1.000 1.000 1.000 0.999 0.996 0.968 0.867 0.647 0.346 0.206 0.099 0.006 0.000 0.0009 1.000 1.000 1.000 1.000 1.000 0.999 0.992 0.954 0.831 0.579 0.416 0.253 0.034 0.003 0.000
10 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.989 0.942 0.798 0.667 0.498 0.134 0.025 0.00011 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.987 0.936 0.873 0.766 0.379 0.135 0.00712 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.990 0.976 0.945 0.746 0.487 0.12213 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 14 0 0.869 0.488 0.229 0.044 0.018 0.007 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.992 0.847 0.585 0.198 0.101 0.047 0.008 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.970 0.842 0.448 0.281 0.161 0.040 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.996 0.956 0.698 0.521 0.355 0.124 0.029 0.004 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 1.000 0.991 0.870 0.742 0.584 0.279 0.090 0.018 0.002 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.999 0.956 0.888 0.781 0.486 0.212 0.058 0.008 0.002 0.000 0.000 0.000 0.0006 1.000 1.000 1.000 0.988 0.962 0.907 0.692 0.395 0.150 0.031 0.010 0.002 0.000 0.000 0.0007 1.000 1.000 1.000 0.998 0.990 0.969 0.850 0.605 0.308 0.093 0.038 0.012 0.000 0.000 0.0008 1.000 1.000 1.000 1.000 0.998 0.992 0.942 0.788 0.514 0.219 0.112 0.044 0.001 0.000 0.0009 1.000 1.000 1.000 1.000 1.000 0.998 0.982 0.910 0.721 0.416 0.258 0.130 0.009 0.000 0.000
10 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.971 0.876 0.645 0.479 0.302 0.044 0.004 0.00011 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.960 0.839 0.719 0.552 0.158 0.030 0.00012 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.992 0.953 0.899 0.802 0.415 0.153 0.00813 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.993 0.982 0.956 0.771 0.512 0.13114 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 4
Tabla 1C. Probabilidades acumuladas p de la distribución binomial (n = 15, 16, 17, 18).ϕ
x 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99n = 15 0 0.860 0.463 0.206 0.035 0.013 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.990 0.829 0.549 0.167 0.080 0.035 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 1.000 0.964 0.816 0.398 0.236 0.127 0.027 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.995 0.944 0.648 0.461 0.297 0.091 0.018 0.002 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.999 0.987 0.836 0.686 0.515 0.217 0.059 0.009 0.001 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.998 0.939 0.852 0.722 0.403 0.151 0.034 0.004 0.001 0.000 0.000 0.000 0.0006 1.000 1.000 1.000 0.982 0.943 0.869 0.610 0.304 0.095 0.015 0.004 0.001 0.000 0.000 0.0007 1.000 1.000 1.000 0.996 0.983 0.950 0.787 0.500 0.213 0.050 0.017 0.004 0.000 0.000 0.0008 1.000 1.000 1.000 0.999 0.996 0.985 0.905 0.696 0.390 0.131 0.057 0.018 0.000 0.000 0.0009 1.000 1.000 1.000 1.000 0.999 0.996 0.966 0.849 0.597 0.278 0.148 0.061 0.002 0.000 0.000
10 1.000 1.000 1.000 1.000 1.000 0.999 0.991 0.941 0.783 0.485 0.314 0.164 0.013 0.001 0.00011 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.982 0.909 0.703 0.539 0.352 0.056 0.005 0.00012 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.973 0.873 0.764 0.602 0.184 0.036 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.965 0.920 0.833 0.451 0.171 0.01014 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.987 0.965 0.794 0.537 0.14015 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 16 0 0.851 0.440 0.185 0.028 0.010 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.989 0.811 0.515 0.141 0.063 0.026 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.957 0.789 0.352 0.197 0.099 0.018 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.993 0.932 0.598 0.405 0.246 0.065 0.011 0.001 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.999 0.983 0.798 0.630 0.450 0.167 0.038 0.005 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.997 0.918 0.810 0.660 0.329 0.105 0.019 0.002 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.999 0.973 0.920 0.825 0.527 0.227 0.058 0.007 0.002 0.000 0.000 0.000 0.0007 1.000 1.000 1.000 0.993 0.973 0.926 0.716 0.402 0.142 0.026 0.007 0.001 0.000 0.000 0.0008 1.000 1.000 1.000 0.999 0.993 0.974 0.858 0.598 0.284 0.074 0.027 0.007 0.000 0.000 0.0009 1.000 1.000 1.000 1.000 0.998 0.993 0.942 0.773 0.473 0.175 0.080 0.027 0.001 0.000 0.000
10 1.000 1.000 1.000 1.000 1.000 0.998 0.981 0.895 0.671 0.340 0.190 0.082 0.003 0.000 0.00011 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.962 0.833 0.550 0.370 0.202 0.017 0.001 0.00012 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.989 0.935 0.754 0.595 0.402 0.068 0.007 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.982 0.901 0.803 0.648 0.211 0.043 0.00114 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.974 0.937 0.859 0.485 0.189 0.01115 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.990 0.972 0.815 0.560 0.14916 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 17 0 0.843 0.418 0.167 0.023 0.008 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.988 0.792 0.482 0.118 0.050 0.019 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.950 0.762 0.310 0.164 0.077 0.012 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.991 0.917 0.549 0.353 0.202 0.046 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.999 0.978 0.758 0.574 0.389 0.126 0.025 0.003 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.995 0.894 0.765 0.597 0.264 0.072 0.011 0.001 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.999 0.962 0.893 0.775 0.448 0.166 0.035 0.003 0.001 0.000 0.000 0.000 0.0007 1.000 1.000 1.000 0.989 0.960 0.895 0.641 0.315 0.092 0.013 0.003 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.997 0.988 0.960 0.801 0.500 0.199 0.040 0.012 0.003 0.000 0.000 0.0009 1.000 1.000 1.000 1.000 0.997 0.987 0.908 0.685 0.359 0.105 0.040 0.011 0.000 0.000 0.000
10 1.000 1.000 1.000 1.000 0.999 0.997 0.965 0.834 0.552 0.225 0.107 0.038 0.001 0.000 0.00011 1.000 1.000 1.000 1.000 1.000 0.999 0.989 0.928 0.736 0.403 0.235 0.106 0.005 0.000 0.00012 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.975 0.874 0.611 0.426 0.242 0.022 0.001 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.954 0.798 0.647 0.451 0.083 0.009 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.988 0.923 0.836 0.690 0.238 0.050 0.00115 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.981 0.950 0.882 0.518 0.208 0.01216 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.992 0.977 0.833 0.582 0.15717 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 18 0 0.835 0.397 0.150 0.018 0.006 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.986 0.774 0.450 0.099 0.039 0.014 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.942 0.734 0.271 0.135 0.060 0.008 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.989 0.902 0.501 0.306 0.165 0.033 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.998 0.972 0.716 0.519 0.333 0.094 0.015 0.001 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.994 0.867 0.717 0.534 0.209 0.048 0.006 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.999 0.949 0.861 0.722 0.374 0.119 0.020 0.001 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 1.000 0.984 0.943 0.859 0.563 0.240 0.058 0.006 0.001 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.996 0.981 0.940 0.737 0.407 0.135 0.021 0.005 0.001 0.000 0.000 0.0009 1.000 1.000 1.000 0.999 0.995 0.979 0.865 0.593 0.263 0.060 0.019 0.004 0.000 0.000 0.000
10 1.000 1.000 1.000 1.000 0.999 0.994 0.942 0.760 0.437 0.141 0.057 0.016 0.000 0.000 0.00011 1.000 1.000 1.000 1.000 1.000 0.999 0.980 0.881 0.626 0.278 0.139 0.051 0.001 0.000 0.00012 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.952 0.791 0.466 0.283 0.133 0.006 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.985 0.906 0.667 0.481 0.284 0.028 0.002 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.967 0.835 0.694 0.499 0.098 0.011 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.992 0.940 0.865 0.729 0.266 0.058 0.00116 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.986 0.961 0.901 0.550 0.226 0.01417 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.994 0.982 0.850 0.603 0.16518 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 5
Tabla 1D. Probabilidades acumuladas p de la distribución binomial (n = 19, 20, 21).
ϕx 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99
n = 19 0 0.826 0.377 0.135 0.014 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.985 0.755 0.420 0.083 0.031 0.010 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.933 0.705 0.237 0.111 0.046 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.987 0.885 0.455 0.263 0.133 0.023 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.998 0.965 0.673 0.465 0.282 0.070 0.010 0.001 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.991 0.837 0.668 0.474 0.163 0.032 0.003 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.998 0.932 0.825 0.666 0.308 0.084 0.012 0.001 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 1.000 0.977 0.923 0.818 0.488 0.180 0.035 0.003 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.993 0.971 0.916 0.667 0.324 0.088 0.011 0.002 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.998 0.991 0.967 0.814 0.500 0.186 0.033 0.009 0.002 0.000 0.000 0.000
10 1.000 1.000 1.000 1.000 0.998 0.989 0.912 0.676 0.333 0.084 0.029 0.007 0.000 0.000 0.00011 1.000 1.000 1.000 1.000 1.000 0.997 0.965 0.820 0.512 0.182 0.077 0.023 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 1.000 0.999 0.988 0.916 0.692 0.334 0.175 0.068 0.002 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.968 0.837 0.526 0.332 0.163 0.009 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.990 0.930 0.718 0.535 0.327 0.035 0.002 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.977 0.867 0.737 0.545 0.115 0.013 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.954 0.889 0.763 0.295 0.067 0.00117 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.990 0.969 0.917 0.580 0.245 0.01518 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.986 0.865 0.623 0.17419 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 20 0 0.818 0.358 0.122 0.012 0.003 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.983 0.736 0.392 0.069 0.024 0.008 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.925 0.677 0.206 0.091 0.035 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.984 0.867 0.411 0.225 0.107 0.016 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.997 0.957 0.630 0.415 0.238 0.051 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.989 0.804 0.617 0.416 0.126 0.021 0.002 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.998 0.913 0.786 0.608 0.250 0.058 0.006 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 1.000 0.968 0.898 0.772 0.416 0.132 0.021 0.001 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.990 0.959 0.887 0.596 0.252 0.057 0.005 0.001 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.997 0.986 0.952 0.755 0.412 0.128 0.017 0.004 0.001 0.000 0.000 0.000
10 1.000 1.000 1.000 0.999 0.996 0.983 0.872 0.588 0.245 0.048 0.014 0.003 0.000 0.000 0.00011 1.000 1.000 1.000 1.000 0.999 0.995 0.943 0.748 0.404 0.113 0.041 0.010 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 1.000 0.999 0.979 0.868 0.584 0.228 0.102 0.032 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.942 0.750 0.392 0.214 0.087 0.002 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.979 0.874 0.584 0.383 0.196 0.011 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.949 0.762 0.585 0.370 0.043 0.003 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.984 0.893 0.775 0.589 0.133 0.016 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.965 0.909 0.794 0.323 0.075 0.00118 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.992 0.976 0.931 0.608 0.264 0.01719 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.997 0.988 0.878 0.642 0.18220 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 21 0 0.810 0.341 0.109 0.009 0.002 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.981 0.717 0.365 0.058 0.019 0.006 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.915 0.648 0.179 0.075 0.027 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.981 0.848 0.370 0.192 0.086 0.011 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.997 0.948 0.586 0.367 0.198 0.037 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 1.000 0.986 0.769 0.567 0.363 0.096 0.013 0.001 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.997 0.891 0.744 0.551 0.200 0.039 0.004 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 0.999 0.957 0.870 0.723 0.350 0.095 0.012 0.001 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.986 0.944 0.852 0.524 0.192 0.035 0.002 0.000 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.996 0.979 0.932 0.691 0.332 0.085 0.009 0.002 0.000 0.000 0.000 0.000
10 1.000 1.000 1.000 0.999 0.994 0.974 0.826 0.500 0.174 0.026 0.006 0.001 0.000 0.000 0.00011 1.000 1.000 1.000 1.000 0.998 0.991 0.915 0.668 0.309 0.068 0.021 0.004 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 1.000 0.998 0.965 0.808 0.476 0.148 0.056 0.014 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 0.999 0.988 0.905 0.650 0.277 0.130 0.043 0.001 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.961 0.800 0.449 0.256 0.109 0.003 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.987 0.904 0.637 0.433 0.231 0.014 0.000 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.963 0.802 0.633 0.414 0.052 0.003 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.989 0.914 0.808 0.630 0.152 0.019 0.00018 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.973 0.925 0.821 0.352 0.085 0.00119 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.981 0.942 0.635 0.283 0.01920 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.991 0.891 0.659 0.19021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 6
Tabla 1E. Probabilidades acumuladas de la distribución binomial (n = 22, 23).
ϕx 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99
n = 22 0 0.802 0.324 0.098 0.007 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.980 0.698 0.339 0.048 0.015 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.999 0.905 0.620 0.154 0.061 0.021 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.978 0.828 0.332 0.162 0.068 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.996 0.938 0.543 0.323 0.165 0.027 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 0.999 0.982 0.733 0.517 0.313 0.072 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.996 0.867 0.699 0.494 0.158 0.026 0.002 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 0.999 0.944 0.838 0.671 0.290 0.067 0.007 0.000 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.980 0.925 0.814 0.454 0.143 0.021 0.001 0.000 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.994 0.970 0.908 0.624 0.262 0.055 0.004 0.001 0.000 0.000 0.000 0.000
10 1.000 1.000 1.000 0.998 0.990 0.961 0.772 0.416 0.121 0.014 0.003 0.000 0.000 0.000 0.00011 1.000 1.000 1.000 1.000 0.997 0.986 0.879 0.584 0.228 0.039 0.010 0.002 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 0.999 0.996 0.945 0.738 0.376 0.092 0.030 0.006 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 0.999 0.979 0.857 0.546 0.186 0.075 0.020 0.000 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.933 0.710 0.329 0.162 0.056 0.001 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.974 0.842 0.506 0.301 0.133 0.004 0.000 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.928 0.687 0.483 0.267 0.018 0.001 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.973 0.835 0.677 0.457 0.062 0.004 0.00018 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.932 0.838 0.668 0.172 0.022 0.00019 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.979 0.939 0.846 0.380 0.095 0.00120 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.985 0.952 0.661 0.302 0.02021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.993 0.902 0.676 0.19822 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 23 0 0.794 0.307 0.089 0.006 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.978 0.679 0.315 0.040 0.012 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.998 0.895 0.592 0.133 0.049 0.016 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.974 0.807 0.297 0.137 0.054 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.995 0.927 0.501 0.283 0.136 0.019 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 0.999 0.977 0.695 0.468 0.269 0.054 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.994 0.840 0.654 0.440 0.124 0.017 0.001 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 0.999 0.928 0.804 0.618 0.237 0.047 0.004 0.000 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.973 0.904 0.771 0.388 0.105 0.013 0.001 0.000 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.991 0.959 0.880 0.556 0.202 0.035 0.002 0.000 0.000 0.000 0.000 0.000
10 1.000 1.000 1.000 0.997 0.985 0.945 0.713 0.339 0.081 0.007 0.001 0.000 0.000 0.000 0.00011 1.000 1.000 1.000 0.999 0.995 0.979 0.836 0.500 0.164 0.021 0.005 0.001 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 0.999 0.993 0.919 0.661 0.287 0.055 0.015 0.003 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 1.000 0.998 0.965 0.798 0.444 0.120 0.041 0.009 0.000 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 0.999 0.987 0.895 0.612 0.229 0.096 0.027 0.000 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.953 0.763 0.382 0.196 0.072 0.001 0.000 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.983 0.876 0.560 0.346 0.160 0.006 0.000 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.946 0.731 0.532 0.305 0.023 0.001 0.00018 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.981 0.864 0.717 0.499 0.073 0.005 0.00019 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.946 0.863 0.703 0.193 0.026 0.00020 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.984 0.951 0.867 0.408 0.105 0.00221 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.988 0.960 0.685 0.321 0.02222 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.911 0.693 0.20623 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 7
Tabla 1F. Probabilidades acumuladas de la distribución binomial (n = 24, 25).
ϕx 0.01 0.05 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 0.95 0.99
n = 24 0 0.786 0.292 0.080 0.005 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.976 0.661 0.292 0.033 0.009 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.998 0.884 0.564 0.115 0.040 0.012 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.970 0.786 0.264 0.115 0.042 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.994 0.915 0.460 0.247 0.111 0.013 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 0.999 0.972 0.656 0.422 0.229 0.040 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.993 0.811 0.607 0.389 0.096 0.011 0.001 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 0.998 0.911 0.766 0.565 0.192 0.032 0.002 0.000 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.964 0.879 0.725 0.328 0.076 0.008 0.000 0.000 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.987 0.945 0.847 0.489 0.154 0.022 0.001 0.000 0.000 0.000 0.000 0.000
10 1.000 1.000 1.000 0.996 0.979 0.926 0.650 0.271 0.053 0.004 0.001 0.000 0.000 0.000 0.00011 1.000 1.000 1.000 0.999 0.993 0.969 0.787 0.419 0.114 0.012 0.002 0.000 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 0.998 0.988 0.886 0.581 0.213 0.031 0.007 0.001 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 0.999 0.996 0.947 0.729 0.350 0.074 0.021 0.004 0.000 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 0.999 0.978 0.846 0.511 0.153 0.055 0.013 0.000 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.924 0.672 0.275 0.121 0.036 0.000 0.000 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.968 0.808 0.435 0.234 0.089 0.002 0.000 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.989 0.904 0.611 0.393 0.189 0.007 0.000 0.00018 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.960 0.771 0.578 0.344 0.028 0.001 0.00019 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.987 0.889 0.753 0.540 0.085 0.006 0.00020 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.958 0.885 0.736 0.214 0.030 0.00021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.988 0.960 0.885 0.436 0.116 0.00222 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.991 0.967 0.708 0.339 0.02423 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.995 0.920 0.708 0.21424 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
n = 25 0 0.778 0.277 0.072 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 0.974 0.642 0.271 0.027 0.007 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0002 0.998 0.873 0.537 0.098 0.032 0.009 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0003 1.000 0.966 0.764 0.234 0.096 0.033 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0004 1.000 0.993 0.902 0.421 0.214 0.090 0.009 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0005 1.000 0.999 0.967 0.617 0.378 0.193 0.029 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 1.000 1.000 0.991 0.780 0.561 0.341 0.074 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.0007 1.000 1.000 0.998 0.891 0.727 0.512 0.154 0.022 0.001 0.000 0.000 0.000 0.000 0.000 0.0008 1.000 1.000 1.000 0.953 0.851 0.677 0.274 0.054 0.004 0.000 0.000 0.000 0.000 0.000 0.0009 1.000 1.000 1.000 0.983 0.929 0.811 0.425 0.115 0.013 0.000 0.000 0.000 0.000 0.000 0.000
10 1.000 1.000 1.000 0.994 0.970 0.902 0.586 0.212 0.034 0.002 0.000 0.000 0.000 0.000 0.00011 1.000 1.000 1.000 0.998 0.989 0.956 0.732 0.345 0.078 0.006 0.001 0.000 0.000 0.000 0.00012 1.000 1.000 1.000 1.000 0.997 0.983 0.846 0.500 0.154 0.017 0.003 0.000 0.000 0.000 0.00013 1.000 1.000 1.000 1.000 0.999 0.994 0.922 0.655 0.268 0.044 0.011 0.002 0.000 0.000 0.00014 1.000 1.000 1.000 1.000 1.000 0.998 0.966 0.788 0.414 0.098 0.030 0.006 0.000 0.000 0.00015 1.000 1.000 1.000 1.000 1.000 1.000 0.987 0.885 0.575 0.189 0.071 0.017 0.000 0.000 0.00016 1.000 1.000 1.000 1.000 1.000 1.000 0.996 0.946 0.726 0.323 0.149 0.047 0.000 0.000 0.00017 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.978 0.846 0.488 0.273 0.109 0.002 0.000 0.00018 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.993 0.926 0.659 0.439 0.220 0.009 0.000 0.00019 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.971 0.807 0.622 0.383 0.033 0.001 0.00020 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.991 0.910 0.786 0.579 0.098 0.007 0.00021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.967 0.904 0.766 0.236 0.034 0.00022 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.991 0.968 0.902 0.463 0.127 0.00223 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.993 0.973 0.729 0.358 0.02624 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.928 0.723 0.22224 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 8
2. Distribución Poisson
X ∼ Poisson(λ)
p = P (X ≤ x) =x∑
k=0
λke−λ
k!= 1− α
0 x
p α
Tabla 2A. Probabilidades acumuladas p de la distribución Poisson.
λx 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00 0.905 0.819 0.741 0.670 0.607 0.549 0.497 0.449 0.407 0.3681 0.995 0.982 0.963 0.938 0.910 0.878 0.844 0.809 0.772 0.7362 1.000 0.999 0.996 0.992 0.986 0.977 0.966 0.953 0.937 0.9203 1.000 1.000 1.000 0.999 0.998 0.997 0.994 0.991 0.987 0.9814 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.9965 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.9996 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Tabla 2B. Probabilidades acumuladas p de la distribución Poisson.
λx 2 3 4 5 6 7 8 9 10 15 200 0.135 0.050 0.018 0.007 0.002 0.001 0.000 0.000 0.000 0.000 0.0001 0.406 0.199 0.092 0.040 0.017 0.007 0.003 0.001 0.000 0.000 0.0002 0.677 0.423 0.238 0.125 0.062 0.030 0.014 0.006 0.003 0.000 0.0003 0.857 0.647 0.433 0.265 0.151 0.082 0.042 0.021 0.010 0.000 0.0004 0.947 0.815 0.629 0.440 0.285 0.173 0.100 0.055 0.029 0.001 0.0005 0.983 0.916 0.785 0.616 0.446 0.301 0.191 0.116 0.067 0.003 0.0006 0.995 0.966 0.889 0.762 0.606 0.450 0.313 0.207 0.130 0.008 0.0007 0.999 0.988 0.949 0.867 0.744 0.599 0.453 0.324 0.220 0.018 0.0018 1.000 0.996 0.979 0.932 0.847 0.729 0.593 0.456 0.333 0.037 0.0029 1.000 0.999 0.992 0.968 0.916 0.830 0.717 0.587 0.458 0.070 0.005
10 1.000 1.000 0.997 0.986 0.957 0.901 0.816 0.706 0.583 0.118 0.01111 1.000 1.000 0.999 0.995 0.980 0.947 0.888 0.803 0.697 0.185 0.02112 1.000 1.000 1.000 0.998 0.991 0.973 0.936 0.876 0.792 0.268 0.03913 1.000 1.000 1.000 0.999 0.996 0.987 0.966 0.926 0.864 0.363 0.06614 1.000 1.000 1.000 1.000 0.999 0.994 0.983 0.959 0.917 0.466 0.10515 1.000 1.000 1.000 1.000 0.999 0.998 0.992 0.978 0.951 0.568 0.15716 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.989 0.973 0.664 0.22117 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.995 0.986 0.749 0.29718 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.993 0.819 0.38119 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.997 0.875 0.47020 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.917 0.55921 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.947 0.64422 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.967 0.72123 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.981 0.78724 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.989 0.84325 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.88826 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.92227 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.94828 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.96629 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.97830 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.98731 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99232 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99533 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99734 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99935 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99936 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 9
3. Distribución Normal Estándar
Z ∼ N(0, 1)
p = P (Z ≤ z) =∫ z−∞
φZ(u)du = 1− α
dondeφZ(u) =
1√2π
e−12 u
2
0 z
p α
Nota: Si X ∼ N(µ, σ2), entonces Z = (X − µ)/σ ∼ N(0, 1). Luego,
P (X ≤ x) = P(
Z ≤ x− µσ
)
Tabla 3A. Probabilidades acumuladas p de la distribución normal estándar.
z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00−3.4 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003−3.3 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005−3.2 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007−3.1 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010−3.0 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013−2.9 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019−2.8 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026−2.7 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035−2.6 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047−2.5 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062−2.4 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082−2.3 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107−2.2 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139−2.1 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179−2.0 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228−1.9 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287−1.8 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359−1.7 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446−1.6 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548−1.5 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668−1.4 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 0.0808−1.3 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968−1.2 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151−1.1 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357−1.0 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587−0.9 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841−0.8 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119−0.7 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420−0.6 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743−0.5 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085−0.4 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446−0.3 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821−0.2 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207−0.1 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602−0.0 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 10
Tabla 3B. Probabilidades acumuladas p de la distribución normal estándar.
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 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 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 0.9032 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 0.9382 0.9394 0.9406 0.9418 0.9429 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 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.99973.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 11
4. Distribución Gamma
X ∼ Γ(κ, 1)
p = P (X ≤ x) =∫ x
0
φΓ(u)du = 1− α
dondeφΓ(u) =
1Γ(κ)
uκ−1e−u
0 x
p α
Nota: Si Y ∼ Γ(κ, λ), entonces, X = λY ∼ Γ(κ, 1). Luego,
P (Y ≤ y) = P (X ≤ λy)
Tabla 4. Probabilidades acumuladas p de la distribución
κx 1 2 3 4 5 6 7 8 9 10 15 20
0.1 0.095 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000.5 0.393 0.090 0.014 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1 0.632 0.264 0.080 0.019 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.0002 0.865 0.594 0.323 0.143 0.053 0.017 0.005 0.001 0.000 0.000 0.000 0.0003 0.950 0.801 0.577 0.353 0.185 0.084 0.034 0.012 0.004 0.001 0.000 0.0004 0.982 0.908 0.762 0.567 0.371 0.215 0.111 0.051 0.021 0.008 0.000 0.0005 0.993 0.960 0.875 0.735 0.560 0.384 0.238 0.133 0.068 0.032 0.000 0.0006 0.998 0.983 0.938 0.849 0.715 0.554 0.394 0.256 0.153 0.084 0.001 0.0007 0.999 0.993 0.970 0.918 0.827 0.699 0.550 0.401 0.271 0.170 0.006 0.0008 1.000 0.997 0.986 0.958 0.900 0.809 0.687 0.547 0.407 0.283 0.017 0.0009 1.000 0.999 0.994 0.979 0.945 0.884 0.793 0.676 0.544 0.413 0.041 0.001
10 1.000 1.000 0.997 0.990 0.971 0.933 0.870 0.780 0.667 0.542 0.083 0.00311 1.000 1.000 0.999 0.995 0.985 0.962 0.921 0.857 0.768 0.659 0.146 0.00912 1.000 1.000 0.999 0.998 0.992 0.980 0.954 0.910 0.845 0.758 0.228 0.02113 1.000 1.000 1.000 0.999 0.996 0.989 0.974 0.946 0.900 0.834 0.325 0.04314 1.000 1.000 1.000 1.000 0.998 0.994 0.986 0.968 0.938 0.891 0.430 0.07715 1.000 1.000 1.000 1.000 0.999 0.997 0.992 0.982 0.963 0.930 0.534 0.12516 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.990 0.978 0.957 0.632 0.18817 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.995 0.987 0.974 0.719 0.26418 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.997 0.993 0.985 0.792 0.34919 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.996 0.991 0.850 0.43920 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.995 0.895 0.53021 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.997 0.928 0.61622 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.952 0.69423 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.969 0.76224 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.980 0.82025 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.988 0.86626 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.992 0.90327 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.93128 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.997 0.95229 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.96730 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.97831 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.98632 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99133 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99434 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99635 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99836 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99937 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99938 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.99939 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 12
5. Distribución t de Student
T ∼ tν
p = P (T ≤ t) =∫ t−∞
φT (u)du = 1− α
donde
φT (u) =1√νπ
Γ(
ν+12
)
Γ(
ν2
)(
1 +u2
ν
)− ν+120
p α
Tabla 5. Valores cŕıticos t(α;ν) de la distribución t de Student.
p0.75 0.80 0.90 0.95 0.975 0.99 0.995 0.999 0.9995 0.9999
αν 0.25 0.20 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 0.00011 1.000 1.376 3.078 6.314 12.706 31.821 63.657 318.309 636.619 3183.0992 0.816 1.061 1.886 2.920 4.303 6.965 9.925 22.327 31.599 70.7003 0.765 0.978 1.638 2.353 3.182 4.541 5.841 10.215 12.924 22.2044 0.741 0.941 1.533 2.132 2.776 3.747 4.604 7.173 8.610 13.0345 0.727 0.920 1.476 2.015 2.571 3.365 4.032 5.893 6.869 9.6786 0.718 0.906 1.440 1.943 2.447 3.143 3.707 5.208 5.959 8.0257 0.711 0.896 1.415 1.895 2.365 2.998 3.499 4.785 5.408 7.0638 0.706 0.889 1.397 1.860 2.306 2.896 3.355 4.501 5.041 6.4429 0.703 0.883 1.383 1.833 2.262 2.821 3.250 4.297 4.781 6.010
10 0.700 0.879 1.372 1.812 2.228 2.764 3.169 4.144 4.587 5.69411 0.697 0.876 1.363 1.796 2.201 2.718 3.106 4.025 4.437 5.45312 0.695 0.873 1.356 1.782 2.179 2.681 3.055 3.930 4.318 5.26313 0.694 0.870 1.350 1.771 2.160 2.650 3.012 3.852 4.221 5.11114 0.692 0.868 1.345 1.761 2.145 2.624 2.977 3.787 4.140 4.98515 0.691 0.866 1.341 1.753 2.131 2.602 2.947 3.733 4.073 4.88016 0.690 0.865 1.337 1.746 2.120 2.583 2.921 3.686 4.015 4.79117 0.689 0.863 1.333 1.740 2.110 2.567 2.898 3.646 3.965 4.71418 0.688 0.862 1.330 1.734 2.101 2.552 2.878 3.610 3.922 4.64819 0.688 0.861 1.328 1.729 2.093 2.539 2.861 3.579 3.883 4.59020 0.687 0.860 1.325 1.725 2.086 2.528 2.845 3.552 3.850 4.53921 0.686 0.859 1.323 1.721 2.080 2.518 2.831 3.527 3.819 4.49322 0.686 0.858 1.321 1.717 2.074 2.508 2.819 3.505 3.792 4.45223 0.685 0.858 1.319 1.714 2.069 2.500 2.807 3.485 3.768 4.41524 0.685 0.857 1.318 1.711 2.064 2.492 2.797 3.467 3.745 4.38225 0.684 0.856 1.316 1.708 2.060 2.485 2.787 3.450 3.725 4.35226 0.684 0.856 1.315 1.706 2.056 2.479 2.779 3.435 3.707 4.32427 0.684 0.855 1.314 1.703 2.052 2.473 2.771 3.421 3.690 4.29928 0.683 0.855 1.313 1.701 2.048 2.467 2.763 3.408 3.674 4.27529 0.683 0.854 1.311 1.699 2.045 2.462 2.756 3.396 3.659 4.25430 0.683 0.854 1.310 1.697 2.042 2.457 2.750 3.385 3.646 4.23440 0.681 0.851 1.303 1.684 2.021 2.423 2.704 3.307 3.551 4.09450 0.679 0.849 1.299 1.676 2.009 2.403 2.678 3.261 3.496 4.01475 0.678 0.846 1.293 1.665 1.992 2.377 2.643 3.202 3.425 3.911
100 0.677 0.845 1.290 1.660 1.984 2.364 2.626 3.174 3.390 3.862125 0.676 0.845 1.288 1.657 1.979 2.357 2.616 3.157 3.370 3.832∞ 0.674 0.842 1.282 1.645 1.960 2.326 2.576 3.090 3.291 3.719
c© E. Barrios y J. A. Garćıa v. 0.90
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Tablas de Probabilidades 13
6. Distribución χ2 Ji-Cuadrada
X ∼ χ2ν
p = P (X ≤ x) =∫ x
0
φχ2(u)du = 1− α
donde
φχ2(u) =1
2ν/2Γ (ν/2)uν/2−1e−u/2
0 x
p α
Tabla 6. Valores cŕıticos χ2(α;ν) de la distribución χ2ν Ji-Cuadrada.
p0.005 0.01 0.025 0.05 0.1 0.90 0.95 0.975 0.99 0.995
αν 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.0051 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.8792 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.5973 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.8384 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.8605 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.7506 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.5487 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.2788 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.9559 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589
10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.18811 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.75712 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.30013 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.81914 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.31915 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.80116 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.26717 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.71818 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.15619 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.58220 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.99721 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.40122 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.79623 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.18124 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.55925 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.92826 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.29027 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.64528 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.99329 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.33630 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.67231 14.458 15.655 17.539 19.281 21.434 41.422 44.985 48.232 52.191 55.00332 15.134 16.362 18.291 20.072 22.271 42.585 46.194 49.480 53.486 56.32833 15.815 17.074 19.047 20.867 23.110 43.745 47.400 50.725 54.776 57.64834 16.501 17.789 19.806 21.664 23.952 44.903 48.602 51.966 56.061 58.96435 17.192 18.509 20.569 22.465 24.797 46.059 49.802 53.203 57.342 60.27536 17.887 19.233 21.336 23.269 25.643 47.212 50.998 54.437 58.619 61.58137 18.586 19.960 22.106 24.075 26.492 48.363 52.192 55.668 59.893 62.88338 19.289 20.691 22.878 24.884 27.343 49.513 53.384 56.896 61.162 64.18139 19.996 21.426 23.654 25.695 28.196 50.660 54.572 58.120 62.428 65.47640 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.76650 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.49075 47.206 49.475 52.942 56.054 59.795 91.061 96.217 100.839 106.393 110.286
100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 14
7. Distribución F
F ∼ Fν1,ν2
p = P (F ≤ f) =∫ f
0
φF (u)du = 1− α
donde
φF (u) =Γ
(ν1+ν2
2
)ν
ν1/21 ν
ν2/22
Γ(ν1/2)Γ(ν2/2)u(ν1/2)−1(ν2 + ν1u)−(ν1+ν2)/2 0 f
p α
Nota: Si F ∼ Fν1,ν2 , entonces,
p = P (F ≤ F(1−α;ν1,ν2)) = P(
F ≤ 1F(α;ν2,ν1)
)= 1− α
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 15
Tab
la7A
.V
alor
escŕ
ıtic
osF
(α;ν
1,ν
2)
dela
dist
ribu
ción
F.
p=
0.9
0α
=0.1
0ν1
ν2
12
34
56
78
910
12
15
20
25
50
75
100
∞1
39.8
649.5
053.5
955.8
357.2
458.2
058.9
159.4
459.8
660.1
960.7
161.2
261.7
462.0
562.6
962.9
063.0
163.3
22
8.5
39.0
09.1
69.2
49.2
99.3
39.3
59.3
79.3
89.3
99.4
19.4
29.4
49.4
59.4
79.4
89.4
89.4
93
5.5
45.4
65.3
95.3
45.3
15.2
85.2
75.2
55.2
45.2
35.2
25.2
05.1
85.1
75.1
55.1
55.1
45.1
34
4.5
44.3
24.1
94.1
14.0
54.0
13.9
83.9
53.9
43.9
23.9
03.8
73.8
43.8
33.8
03.7
83.7
83.7
65
4.0
63.7
83.6
23.5
23.4
53.4
03.3
73.3
43.3
23.3
03.2
73.2
43.2
13.1
93.1
53.1
33.1
33.1
16
3.7
83.4
63.2
93.1
83.1
13.0
53.0
12.9
82.9
62.9
42.9
02.8
72.8
42.8
12.7
72.7
52.7
52.7
27
3.5
93.2
63.0
72.9
62.8
82.8
32.7
82.7
52.7
22.7
02.6
72.6
32.5
92.5
72.5
22.5
12.5
02.4
78
3.4
63.1
12.9
22.8
12.7
32.6
72.6
22.5
92.5
62.5
42.5
02.4
62.4
22.4
02.3
52.3
32.3
22.2
99
3.3
63.0
12.8
12.6
92.6
12.5
52.5
12.4
72.4
42.4
22.3
82.3
42.3
02.2
72.2
22.2
02.1
92.1
610
3.2
92.9
22.7
32.6
12.5
22.4
62.4
12.3
82.3
52.3
22.2
82.2
42.2
02.1
72.1
22.1
02.0
92.0
611
3.2
32.8
62.6
62.5
42.4
52.3
92.3
42.3
02.2
72.2
52.2
12.1
72.1
22.1
02.0
42.0
22.0
11.9
712
3.1
82.8
12.6
12.4
82.3
92.3
32.2
82.2
42.2
12.1
92.1
52.1
02.0
62.0
31.9
71.9
51.9
41.9
013
3.1
42.7
62.5
62.4
32.3
52.2
82.2
32.2
02.1
62.1
42.1
02.0
52.0
11.9
81.9
21.8
91.8
81.8
514
3.1
02.7
32.5
22.3
92.3
12.2
42.1
92.1
52.1
22.1
02.0
52.0
11.9
61.9
31.8
71.8
51.8
31.8
015
3.0
72.7
02.4
92.3
62.2
72.2
12.1
62.1
22.0
92.0
62.0
21.9
71.9
21.8
91.8
31.8
01.7
91.7
616
3.0
52.6
72.4
62.3
32.2
42.1
82.1
32.0
92.0
62.0
31.9
91.9
41.8
91.8
61.7
91.7
71.7
61.7
217
3.0
32.6
42.4
42.3
12.2
22.1
52.1
02.0
62.0
32.0
01.9
61.9
11.8
61.8
31.7
61.7
41.7
31.6
918
3.0
12.6
22.4
22.2
92.2
02.1
32.0
82.0
42.0
01.9
81.9
31.8
91.8
41.8
01.7
41.7
11.7
01.6
619
2.9
92.6
12.4
02.2
72.1
82.1
12.0
62.0
21.9
81.9
61.9
11.8
61.8
11.7
81.7
11.6
91.6
71.6
320
2.9
72.5
92.3
82.2
52.1
62.0
92.0
42.0
01.9
61.9
41.8
91.8
41.7
91.7
61.6
91.6
61.6
51.6
121
2.9
62.5
72.3
62.2
32.1
42.0
82.0
21.9
81.9
51.9
21.8
71.8
31.7
81.7
41.6
71.6
41.6
31.5
922
2.9
52.5
62.3
52.2
22.1
32.0
62.0
11.9
71.9
31.9
01.8
61.8
11.7
61.7
31.6
51.6
31.6
11.5
723
2.9
42.5
52.3
42.2
12.1
12.0
51.9
91.9
51.9
21.8
91.8
41.8
01.7
41.7
11.6
41.6
11.5
91.5
524
2.9
32.5
42.3
32.1
92.1
02.0
41.9
81.9
41.9
11.8
81.8
31.7
81.7
31.7
01.6
21.5
91.5
81.5
325
2.9
22.5
32.3
22.1
82.0
92.0
21.9
71.9
31.8
91.8
71.8
21.7
71.7
21.6
81.6
11.5
81.5
61.5
226
2.9
12.5
22.3
12.1
72.0
82.0
11.9
61.9
21.8
81.8
61.8
11.7
61.7
11.6
71.5
91.5
71.5
51.5
027
2.9
02.5
12.3
02.1
72.0
72.0
01.9
51.9
11.8
71.8
51.8
01.7
51.7
01.6
61.5
81.5
51.5
41.4
928
2.8
92.5
02.2
92.1
62.0
62.0
01.9
41.9
01.8
71.8
41.7
91.7
41.6
91.6
51.5
71.5
41.5
31.4
829
2.8
92.5
02.2
82.1
52.0
61.9
91.9
31.8
91.8
61.8
31.7
81.7
31.6
81.6
41.5
61.5
31.5
21.4
730
2.8
82.4
92.2
82.1
42.0
51.9
81.9
31.8
81.8
51.8
21.7
71.7
21.6
71.6
31.5
51.5
21.5
11.4
640
2.8
42.4
42.2
32.0
92.0
01.9
31.8
71.8
31.7
91.7
61.7
11.6
61.6
11.5
71.4
81.4
51.4
31.3
860
2.7
92.3
92.1
82.0
41.9
51.8
71.8
21.7
71.7
41.7
11.6
61.6
01.5
41.5
01.4
11.3
81.3
61.2
980
2.7
72.3
72.1
52.0
21.9
21.8
51.7
91.7
51.7
11.6
81.6
31.5
71.5
11.4
71.3
81.3
41.3
21.2
5100
2.7
62.3
62.1
42.0
01.9
11.8
31.7
81.7
31.6
91.6
61.6
11.5
61.4
91.4
51.3
51.3
21.2
91.2
2120
2.7
52.3
52.1
31.9
91.9
01.8
21.7
71.7
21.6
81.6
51.6
01.5
51.4
81.4
41.3
41.3
01.2
81.1
9∞
2.7
12.3
02.0
81.9
51.8
51.7
71.7
21.6
71.6
31.6
01.5
51.4
91.4
21.3
81.2
61.2
21.1
91.0
3
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 16
Tab
la7B
.V
alor
escŕ
ıtic
osF
(α;ν
1,ν
2)
dela
dist
ribu
ción
F.
p=
0.9
5α
=0.0
5ν1
ν2
12
34
56
78
910
12
15
20
25
50
75
100
∞1
161.4
5199.5
0215.7
1224.5
8230.1
6233.9
9236.7
7238.8
8240.5
4241.8
8243.9
1245.9
5248.0
1249.2
6251.7
7252.6
2253.0
4254.3
02
18.5
119.0
019.1
619.2
519.3
019.3
319.3
519.3
719.3
819.4
019.4
119.4
319.4
519.4
619.4
819.4
819.4
919.5
03
10.1
39.5
59.2
89.1
29.0
18.9
48.8
98.8
58.8
18.7
98.7
48.7
08.6
68.6
38.5
88.5
68.5
58.5
34
7.7
16.9
46.5
96.3
96.2
66.1
66.0
96.0
46.0
05.9
65.9
15.8
65.8
05.7
75.7
05.6
85.6
65.6
35
6.6
15.7
95.4
15.1
95.0
54.9
54.8
84.8
24.7
74.7
44.6
84.6
24.5
64.5
24.4
44.4
24.4
14.3
76
5.9
95.1
44.7
64.5
34.3
94.2
84.2
14.1
54.1
04.0
64.0
03.9
43.8
73.8
33.7
53.7
33.7
13.6
77
5.5
94.7
44.3
54.1
23.9
73.8
73.7
93.7
33.6
83.6
43.5
73.5
13.4
43.4
03.3
23.2
93.2
73.2
38
5.3
24.4
64.0
73.8
43.6
93.5
83.5
03.4
43.3
93.3
53.2
83.2
23.1
53.1
13.0
22.9
92.9
72.9
39
5.1
24.2
63.8
63.6
33.4
83.3
73.2
93.2
33.1
83.1
43.0
73.0
12.9
42.8
92.8
02.7
72.7
62.7
110
4.9
64.1
03.7
13.4
83.3
33.2
23.1
43.0
73.0
22.9
82.9
12.8
52.7
72.7
32.6
42.6
02.5
92.5
411
4.8
43.9
83.5
93.3
63.2
03.0
93.0
12.9
52.9
02.8
52.7
92.7
22.6
52.6
02.5
12.4
72.4
62.4
112
4.7
53.8
93.4
93.2
63.1
13.0
02.9
12.8
52.8
02.7
52.6
92.6
22.5
42.5
02.4
02.3
72.3
52.3
013
4.6
73.8
13.4
13.1
83.0
32.9
22.8
32.7
72.7
12.6
72.6
02.5
32.4
62.4
12.3
12.2
82.2
62.2
114
4.6
03.7
43.3
43.1
12.9
62.8
52.7
62.7
02.6
52.6
02.5
32.4
62.3
92.3
42.2
42.2
12.1
92.1
315
4.5
43.6
83.2
93.0
62.9
02.7
92.7
12.6
42.5
92.5
42.4
82.4
02.3
32.2
82.1
82.1
42.1
22.0
716
4.4
93.6
33.2
43.0
12.8
52.7
42.6
62.5
92.5
42.4
92.4
22.3
52.2
82.2
32.1
22.0
92.0
72.0
117
4.4
53.5
93.2
02.9
62.8
12.7
02.6
12.5
52.4
92.4
52.3
82.3
12.2
32.1
82.0
82.0
42.0
21.9
618
4.4
13.5
53.1
62.9
32.7
72.6
62.5
82.5
12.4
62.4
12.3
42.2
72.1
92.1
42.0
42.0
01.9
81.9
219
4.3
83.5
23.1
32.9
02.7
42.6
32.5
42.4
82.4
22.3
82.3
12.2
32.1
62.1
12.0
01.9
61.9
41.8
820
4.3
53.4
93.1
02.8
72.7
12.6
02.5
12.4
52.3
92.3
52.2
82.2
02.1
22.0
71.9
71.9
31.9
11.8
421
4.3
23.4
73.0
72.8
42.6
82.5
72.4
92.4
22.3
72.3
22.2
52.1
82.1
02.0
51.9
41.9
01.8
81.8
122
4.3
03.4
43.0
52.8
22.6
62.5
52.4
62.4
02.3
42.3
02.2
32.1
52.0
72.0
21.9
11.8
71.8
51.7
823
4.2
83.4
23.0
32.8
02.6
42.5
32.4
42.3
72.3
22.2
72.2
02.1
32.0
52.0
01.8
81.8
41.8
21.7
624
4.2
63.4
03.0
12.7
82.6
22.5
12.4
22.3
62.3
02.2
52.1
82.1
12.0
31.9
71.8
61.8
21.8
01.7
325
4.2
43.3
92.9
92.7
62.6
02.4
92.4
02.3
42.2
82.2
42.1
62.0
92.0
11.9
61.8
41.8
01.7
81.7
126
4.2
33.3
72.9
82.7
42.5
92.4
72.3
92.3
22.2
72.2
22.1
52.0
71.9
91.9
41.8
21.7
81.7
61.6
927
4.2
13.3
52.9
62.7
32.5
72.4
62.3
72.3
12.2
52.2
02.1
32.0
61.9
71.9
21.8
11.7
61.7
41.6
728
4.2
03.3
42.9
52.7
12.5
62.4
52.3
62.2
92.2
42.1
92.1
22.0
41.9
61.9
11.7
91.7
51.7
31.6
529
4.1
83.3
32.9
32.7
02.5
52.4
32.3
52.2
82.2
22.1
82.1
02.0
31.9
41.8
91.7
71.7
31.7
11.6
430
4.1
73.3
22.9
22.6
92.5
32.4
22.3
32.2
72.2
12.1
62.0
92.0
11.9
31.8
81.7
61.7
21.7
01.6
240
4.0
83.2
32.8
42.6
12.4
52.3
42.2
52.1
82.1
22.0
82.0
01.9
21.8
41.7
81.6
61.6
11.5
91.5
160
4.0
03.1
52.7
62.5
32.3
72.2
52.1
72.1
02.0
41.9
91.9
21.8
41.7
51.6
91.5
61.5
11.4
81.3
980
3.9
63.1
12.7
22.4
92.3
32.2
12.1
32.0
62.0
01.9
51.8
81.7
91.7
01.6
41.5
11.4
51.4
31.3
3100
3.9
43.0
92.7
02.4
62.3
12.1
92.1
02.0
31.9
71.9
31.8
51.7
71.6
81.6
21.4
81.4
21.3
91.2
8120
3.9
23.0
72.6
82.4
52.2
92.1
82.0
92.0
21.9
61.9
11.8
31.7
51.6
61.6
01.4
61.4
01.3
71.2
6∞
3.8
43.0
02.6
12.3
72.2
12.1
02.0
11.9
41.8
81.8
31.7
51.6
71.5
71.5
11.3
51.2
81.2
51.0
3
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 17
Tab
la7C
.V
alor
escŕ
ıtic
osF
(α;ν
1,ν
2)
dela
dist
ribu
ción
F.
p=
0.9
75
α=
0.0
25
ν1
ν2
12
34
56
78
910
12
15
20
25
50
75
100
∞1
648.
799.
864.
900.
922.
937.
948.
957.
963.
969.
977.
985.
993.
998.
1008.
1011.
1013.
1018.
238.5
139.0
039.1
739.2
539.3
039.3
339.3
639.3
739.3
939.4
039.4
139.4
339.4
539.4
639.4
839.4
839.4
939.5
03
17.4
416.0
415.4
415.1
014.8
814.7
314.6
214.5
414.4
714.4
214.3
414.2
514.1
714.1
214.0
113.9
713.9
613.9
04
12.2
210.6
59.9
89.6
09.3
69.2
09.0
78.9
88.9
08.8
48.7
58.6
68.5
68.5
08.3
88.3
48.3
28.2
65
10.0
18.4
37.7
67.3
97.1
56.9
86.8
56.7
66.6
86.6
26.5
26.4
36.3
36.2
76.1
46.1
06.0
86.0
26
8.8
17.2
66.6
06.2
35.9
95.8
25.7
05.6
05.5
25.4
65.3
75.2
75.1
75.1
14.9
84.9
44.9
24.8
57
8.0
76.5
45.8
95.5
25.2
95.1
24.9
94.9
04.8
24.7
64.6
74.5
74.4
74.4
04.2
84.2
34.2
14.1
48
7.5
76.0
65.4
25.0
54.8
24.6
54.5
34.4
34.3
64.3
04.2
04.1
04.0
03.9
43.8
13.7
63.7
43.6
79
7.2
15.7
15.0
84.7
24.4
84.3
24.2
04.1
04.0
33.9
63.8
73.7
73.6
73.6
03.4
73.4
33.4
03.3
310
6.9
45.4
64.8
34.4
74.2
44.0
73.9
53.8
53.7
83.7
23.6
23.5
23.4
23.3
53.2
23.1
83.1
53.0
811
6.7
25.2
64.6
34.2
84.0
43.8
83.7
63.6
63.5
93.5
33.4
33.3
33.2
33.1
63.0
32.9
82.9
62.8
812
6.5
55.1
04.4
74.1
23.8
93.7
33.6
13.5
13.4
43.3
73.2
83.1
83.0
73.0
12.8
72.8
22.8
02.7
313
6.4
14.9
74.3
54.0
03.7
73.6
03.4
83.3
93.3
13.2
53.1
53.0
52.9
52.8
82.7
42.7
02.6
72.6
014
6.3
04.8
64.2
43.8
93.6
63.5
03.3
83.2
93.2
13.1
53.0
52.9
52.8
42.7
82.6
42.5
92.5
62.4
915
6.2
04.7
74.1
53.8
03.5
83.4
13.2
93.2
03.1
23.0
62.9
62.8
62.7
62.6
92.5
52.5
02.4
72.4
016
6.1
24.6
94.0
83.7
33.5
03.3
43.2
23.1
23.0
52.9
92.8
92.7
92.6
82.6
12.4
72.4
22.4
02.3
217
6.0
44.6
24.0
13.6
63.4
43.2
83.1
63.0
62.9
82.9
22.8
22.7
22.6
22.5
52.4
12.3
52.3
32.2
518
5.9
84.5
63.9
53.6
13.3
83.2
23.1
03.0
12.9
32.8
72.7
72.6
72.5
62.4
92.3
52.3
02.2
72.1
919
5.9
24.5
13.9
03.5
63.3
33.1
73.0
52.9
62.8
82.8
22.7
22.6
22.5
12.4
42.3
02.2
42.2
22.1
320
5.8
74.4
63.8
63.5
13.2
93.1
33.0
12.9
12.8
42.7
72.6
82.5
72.4
62.4
02.2
52.2
02.1
72.0
921
5.8
34.4
23.8
23.4
83.2
53.0
92.9
72.8
72.8
02.7
32.6
42.5
32.4
22.3
62.2
12.1
62.1
32.0
422
5.7
94.3
83.7
83.4
43.2
23.0
52.9
32.8
42.7
62.7
02.6
02.5
02.3
92.3
22.1
72.1
22.0
92.0
023
5.7
54.3
53.7
53.4
13.1
83.0
22.9
02.8
12.7
32.6
72.5
72.4
72.3
62.2
92.1
42.0
82.0
61.9
724
5.7
24.3
23.7
23.3
83.1
52.9
92.8
72.7
82.7
02.6
42.5
42.4
42.3
32.2
62.1
12.0
52.0
21.9
425
5.6
94.2
93.6
93.3
53.1
32.9
72.8
52.7
52.6
82.6
12.5
12.4
12.3
02.2
32.0
82.0
22.0
01.9
126
5.6
64.2
73.6
73.3
33.1
02.9
42.8
22.7
32.6
52.5
92.4
92.3
92.2
82.2
12.0
52.0
01.9
71.8
827
5.6
34.2
43.6
53.3
13.0
82.9
22.8
02.7
12.6
32.5
72.4
72.3
62.2
52.1
82.0
31.9
71.9
41.8
528
5.6
14.2
23.6
33.2
93.0
62.9
02.7
82.6
92.6
12.5
52.4
52.3
42.2
32.1
62.0
11.9
51.9
21.8
329
5.5
94.2
03.6
13.2
73.0
42.8
82.7
62.6
72.5
92.5
32.4
32.3
22.2
12.1
41.9
91.9
31.9
01.8
130
5.5
74.1
83.5
93.2
53.0
32.8
72.7
52.6
52.5
72.5
12.4
12.3
12.2
02.1
21.9
71.9
11.8
81.7
940
5.4
24.0
53.4
63.1
32.9
02.7
42.6
22.5
32.4
52.3
92.2
92.1
82.0
71.9
91.8
31.7
71.7
41.6
460
5.2
93.9
33.3
43.0
12.7
92.6
32.5
12.4
12.3
32.2
72.1
72.0
61.9
41.8
71.7
01.6
31.6
01.4
880
5.2
23.8
63.2
82.9
52.7
32.5
72.4
52.3
52.2
82.2
12.1
12.0
01.8
81.8
11.6
31.5
61.5
31.4
0100
5.1
83.8
33.2
52.9
22.7
02.5
42.4
22.3
22.2
42.1
82.0
81.9
71.8
51.7
71.5
91.5
21.4
81.3
5120
5.1
53.8
03.2
32.8
92.6
72.5
22.3
92.3
02.2
22.1
62.0
51.9
41.8
21.7
51.5
61.4
91.4
51.3
1∞
5.0
33.6
93.1
22.7
92.5
72.4
12.2
92.1
92.1
12.0
51.9
51.8
31.7
11.6
31.4
31.3
51.3
01.0
4
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 18
Tab
la7D
.V
alor
escŕ
ıtic
osF
(α;ν
1,ν
2)
dela
dist
ribu
ción
F.
p=
0.9
9α
=0.0
1ν1
ν2
12
34
56
78
910
12
15
20
25
50
75
100
∞1
4052.
4999.
5403.
5625.
5764.
5859.
5928.
5981.
6022.
6056.
6106.
6157.
6209.
6240.
6303.
6324.
6334.
6366.
298.5
099.0
099.1
799.2
599.3
099.3
399.3
699.3
799.3
999.4
099.4
299.4
399.4
599.4
699.4
899.4
999.4
999.5
03
34.1
230.8
229.4
628.7
128.2
427.9
127.6
727.4
927.3
527.2
327.0
526.8
726.6
926.5
826.3
526.2
826.2
426.1
34
21.2
018.0
016.6
915.9
815.5
215.2
114.9
814.8
014.6
614.5
514.3
714.2
014.0
213.9
113.6
913.6
113.5
813.4
65
16.2
613.2
712.0
611.3
910.9
710.6
710.4
610.2
910.1
610.0
59.8
99.7
29.5
59.4
59.2
49.1
79.1
39.0
26
13.7
510.9
29.7
89.1
58.7
58.4
78.2
68.1
07.9
87.8
77.7
27.5
67.4
07.3
07.0
97.0
26.9
96.8
87
12.2
59.5
58.4
57.8
57.4
67.1
96.9
96.8
46.7
26.6
26.4
76.3
16.1
66.0
65.8
65.7
95.7
55.6
58
11.2
68.6
57.5
97.0
16.6
36.3
76.1
86.0
35.9
15.8
15.6
75.5
25.3
65.2
65.0
75.0
04.9
64.8
69
10.5
68.0
26.9
96.4
26.0
65.8
05.6
15.4
75.3
55.2
65.1
14.9
64.8
14.7
14.5
24.4
54.4
14.3
110
10.0
47.5
66.5
55.9
95.6
45.3
95.2
05.0
64.9
44.8
54.7
14.5
64.4
14.3
14.1
24.0
54.0
13.9
111
9.6
57.2
16.2
25.6
75.3
25.0
74.8
94.7
44.6
34.5
44.4
04.2
54.1
04.0
13.8
13.7
43.7
13.6
012
9.3
36.9
35.9
55.4
15.0
64.8
24.6
44.5
04.3
94.3
04.1
64.0
13.8
63.7
63.5
73.5
03.4
73.3
613
9.0
76.7
05.7
45.2
14.8
64.6
24.4
44.3
04.1
94.1
03.9
63.8
23.6
63.5
73.3
83.3
13.2
73.1
714
8.8
66.5
15.5
65.0
44.6
94.4
64.2
84.1
44.0
33.9
43.8
03.6
63.5
13.4
13.2
23.1
53.1
13.0
115
8.6
86.3
65.4
24.8
94.5
64.3
24.1
44.0
03.8
93.8
03.6
73.5
23.3
73.2
83.0
83.0
12.9
82.8
716
8.5
36.2
35.2
94.7
74.4
44.2
04.0
33.8
93.7
83.6
93.5
53.4
13.2
63.1
62.9
72.9
02.8
62.7
517
8.4
06.1
15.1
84.6
74.3
44.1
03.9
33.7
93.6
83.5
93.4
63.3
13.1
63.0
72.8
72.8
02.7
62.6
518
8.2
96.0
15.0
94.5
84.2
54.0
13.8
43.7
13.6
03.5
13.3
73.2
33.0
82.9
82.7
82.7
12.6
82.5
719
8.1
85.9
35.0
14.5
04.1
73.9
43.7
73.6
33.5
23.4
33.3
03.1
53.0
02.9
12.7
12.6
42.6
02.4
920
8.1
05.8
54.9
44.4
34.1
03.8
73.7
03.5
63.4
63.3
73.2
33.0
92.9
42.8
42.6
42.5
72.5
42.4
221
8.0
25.7
84.8
74.3
74.0
43.8
13.6
43.5
13.4
03.3
13.1
73.0
32.8
82.7
92.5
82.5
12.4
82.3
622
7.9
55.7
24.8
24.3
13.9
93.7
63.5
93.4
53.3
53.2
63.1
22.9
82.8
32.7
32.5
32.4
62.4
22.3
123
7.8
85.6
64.7
64.2
63.9
43.7
13.5
43.4
13.3
03.2
13.0
72.9
32.7
82.6
92.4
82.4
12.3
72.2
624
7.8
25.6
14.7
24.2
23.9
03.6
73.5
03.3
63.2
63.1
73.0
32.8
92.7
42.6
42.4
42.3
72.3
32.2
125
7.7
75.5
74.6
84.1
83.8
53.6
33.4
63.3
23.2
23.1
32.9
92.8
52.7
02.6
02.4
02.3
32.2
92.1
726
7.7
25.5
34.6
44.1
43.8
23.5
93.4
23.2
93.1
83.0
92.9
62.8
12.6
62.5
72.3
62.2
92.2
52.1
327
7.6
85.4
94.6
04.1
13.7
83.5
63.3
93.2
63.1
53.0
62.9
32.7
82.6
32.5
42.3
32.2
62.2
22.1
028
7.6
45.4
54.5
74.0
73.7
53.5
33.3
63.2
33.1
23.0
32.9
02.7
52.6
02.5
12.3
02.2
32.1
92.0
729
7.6
05.4
24.5
44.0
43.7
33.5
03.3
33.2
03.0
93.0
02.8
72.7
32.5
72.4
82.2
72.2
02.1
62.0
430
7.5
65.3
94.5
14.0
23.7
03.4
73.3
03.1
73.0
72.9
82.8
42.7
02.5
52.4
52.2
52.1
72.1
32.0
140
7.3
15.1
84.3
13.8
33.5
13.2
93.1
22.9
92.8
92.8
02.6
62.5
22.3
72.2
72.0
61.9
81.9
41.8
160
7.0
84.9
84.1
33.6
53.3
43.1
22.9
52.8
22.7
22.6
32.5
02.3
52.2
02.1
01.8
81.7
91.7
51.6
080
6.9
64.8
84.0
43.5
63.2
63.0
42.8
72.7
42.6
42.5
52.4
22.2
72.1
22.0
11.7
91.7
01.6
51.5
0100
6.9
04.8
23.9
83.5
13.2
12.9
92.8
22.6
92.5
92.5
02.3
72.2
22.0
71.9
71.7
41.6
51.6
01.4
3120
6.8
54.7
93.9
53.4
83.1
72.9
62.7
92.6
62.5
62.4
72.3
42.1
92.0
31.9
31.7
01.6
11.5
61.3
8∞
6.6
44.6
13.7
83.3
23.0
22.8
02.6
42.5
12.4
12.3
22.1
92.0
41.8
81.7
71.5
31.4
21.3
61.0
5
c© E. Barrios y J. A. Garćıa v. 0.90
-
Tablas de Probabilidades 19
Tab
la7E
.V
alor
escŕ
ıtic
osF
(α;ν
1,ν
2)
dela
dist
ribu
ción
F.
p=
0.9
95
α=
0.0
05
ν1
ν2
12
34
56
78
910
12
15
20
25
50
75
100
∞1
16211.
19999.
21615.
22500.
23056.
23437.
23715.
23925.
24091.
24224.
24426.
24630.
24836.
24960.
25211.
25295.
25337.
25463.
2198.5
0199.0
0199.1
7199.2
5199.3
0199.3
3199.3
6199.3
7199.3
9199.4
0199.4
2199.4
3199.4
5199.4
6199.4
8199.4
9199.4
9199.5
03
55.5
549.8
047.4
746.1
945.3
944.8
444.4
344.1
343.8
843.6
943.3
943.0
842.7
842.5
942.2
142.0
942.0
241.8
34
31.3
326.2
824.2
623.1
522.4
621.9
721.6
221.3
521.1
420.9
720.7
020.4
420.1
720.0
019.6
719.5
519.5
019.3
35
22.7
818.3
116.5
315.5
614.9
414.5
114.2
013.9
613.7
713.6
213.3
813.1
512.9
012.7
612.4
512.3
512.3
012.1
56
18.6
314.5
412.9
212.0
311.4
611.0
710.7
910.5
710.3
910.2
510.0
39.8
19.5
99.4
59.1
79.0
79.0
38.8
87
16.2
412.4
010.8
810.0
59.5
29.1
68.8
98.6
88.5
18.3
88.1
87.9
77.7
57.6
27.3
57.2
67.2
27.0
88
14.6
911.0
49.6
08.8
18.3
07.9
57.6
97.5
07.3
47.2
17.0
16.8
16.6
16.4
86.2
26.1
36.0
95.9
59
13.6
110.1
18.7
27.9
67.4
77.1
36.8
86.6
96.5
46.4
26.2
36.0
35.8
35.7
15.4
55.3
75.3
25.1
910
12.8
39.4
38.0
87.3
46.8
76.5
46.3
06.1
25.9
75.8
55.6
65.4
75.2
75.1
54.9
04.8
24.7
74.6
411
12.2
38.9
17.6
06.8
86.4
26.1
05.8
65.6
85.5
45.4
25.2
45.0
54.8
64.7
44.4
94.4
04.3
64.2
312
11.7
58.5
17.2
36.5
26.0
75.7
65.5
25.3
55.2
05.0
94.9
14.7
24.5
34.4
14.1
74.0
84.0
43.9
113
11.3
78.1
96.9
36.2
35.7
95.4
85.2
55.0
84.9
44.8
24.6
44.4
64.2
74.1
53.9
13.8
23.7
83.6
514
11.0
67.9
26.6
86.0
05.5
65.2
65.0
34.8
64.7
24.6
04.4
34.2
54.0
63.9
43.7
03.6
13.5
73.4
415
10.8
07.7
06.4
85.8
05.3
75.0
74.8
54.6
74.5