Distribuci´on χ2P[X≤x] = Rx
−∞
1
2θ/2Γ(θ/2) ·u−1
2θ2·e−u
2du
0.005 0.01 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.25 0.3 0.35 0.4 0.45
1 0.000 0.000 0.001 0.004 0.009 0.016 0.025 0.036 0.049 0.064 0.102 0.148 0.206 0.275 0.357
20.010 0.020 0.051 0.103 0.156 0.211 0.267 0.325 0.385 0.446 0.575 0.713 0.862 1.022 1.196
30.072 0.115 0.216 0.352 0.472 0.584 0.692 0.798 0.902 1.005 1.213 1.424 1.642 1.869 2.109
40.207 0.297 0.484 0.711 0.897 1.064 1.219 1.366 1.509 1.649 1.923 2.195 2.470 2.753 3.047
50.412 0.554 0.831 1.145 1.394 1.610 1.808 1.994 2.171 2.343 2.675 3.000 3.325 3.655 3.996
60.676 0.872 1.237 1.635 1.941 2.204 2.441 2.661 2.870 3.070 3.455 3.828 4.197 4.570 4.952
70.989 1.239 1.690 2.167 2.528 2.833 3.106 3.358 3.596 3.822 4.255 4.671 5.082 5.493 5.913
81.344 1.646 2.180 2.733 3.144 3.490 3.797 4.078 4.342 4.594 5.071 5.527 5.975 6.423 6.877
91.735 2.088 2.700 3.325 3.785 4.168 4.507 4.817 5.106 5.380 5.899 6.393 6.876 7.357 7.843
10 2.156 2.558 3.247 3.940 4.446 4.865 5.234 5.570 5.883 6.179 6.737 7.267 7.783 8.295 8.812
11 2.603 3.053 3.816 4.575 5.124 5.578 5.975 6.336 6.672 6.989 7.584 8.148 8.695 9.237 9.783
12 3.074 3.571 4.404 5.226 5.818 6.304 6.729 7.114 7.471 7.807 8.438 9.034 9.612 10.182 10.755
13 3.565 4.107 5.009 5.892 6.524 7.042 7.493 7.901 8.278 8.634 9.299 9.926 10.532 11.129 11.729
14 4.075 4.660 5.629 6.571 7.242 7.790 8.266 8.696 9.094 9.467 10.165 10.821 11.455 12.078 12.703
15 4.601 5.229 6.262 7.261 7.969 8.547 9.048 9.499 9.916 10.307 11.037 11.721 12.381 13.030 13.679
16 5.142 5.812 6.908 7.962 8.707 9.312 9.837 10.309 10.744 11.152 11.912 12.624 13.310 13.983 14.655
17 5.697 6.408 7.564 8.672 9.452 10.085 10.633 11.125 11.578 12.002 12.792 13.531 14.241 14.937 15.633
18 6.265 7.015 8.231 9.390 10.205 10.865 11.435 11.946 12.417 12.857 13.675 14.440 15.174 15.893 16.611
19 6.844 7.633 8.907 10.117 10.965 11.651 12.242 12.773 13.260 13.716 14.562 15.352 16.109 16.850 17.589
20 7.434 8.260 9.591 10.851 11.732 12.443 13.055 13.604 14.108 14.578 15.452 16.266 17.046 17.809 18.569
21 8.034 8.897 10.283 11.591 12.504 13.240 13.873 14.439 14.959 15.445 16.344 17.182 17.984 18.768 19.548
22 8.643 9.542 10.982 12.338 13.282 14.041 14.695 15.279 15.814 16.314 17.240 18.101 18.924 19.729 20.529
23 9.260 10.196 11.689 13.091 14.065 14.848 15.521 16.122 16.673 17.187 18.137 19.021 19.866 20.690 21.510
24 9.886 10.856 12.401 13.848 14.853 15.659 16.351 16.969 17.534 18.062 19.037 19.943 20.808 21.652 22.491
25 10.520 11.524 13.120 14.611 15.645 16.473 17.184 17.818 18.399 18.940 19.939 20.867 21.752 22.616 23.472
26 11.160 12.198 13.844 15.379 16.441 17.292 18.021 18.671 19.266 19.820 20.843 21.792 22.697 23.579 24.454
27 11.808 12.879 14.573 16.151 17.241 18.114 18.861 19.527 20.136 20.703 21.749 22.719 23.644 24.544 25.437
28 12.461 13.565 15.308 16.928 18.045 18.939 19.704 20.386 21.008 21.588 22.657 23.647 24.591 25.509 26.419
29 13.121 14.256 16.047 17.708 18.853 19.768 20.550 21.247 21.883 22.475 23.567 24.577 25.539 26.475 27.402
30 13.787 14.953 16.791 18.493 19.664 20.599 21.399 22.110 22.760 23.364 24.478 25.508 26.488 27.442 28.386
31 14.458 15.655 17.539 19.281 20.478 21.434 22.250 22.976 23.639 24.255 25.390 26.440 27.438 28.409 29.369
32 15.134 16.362 18.291 20.072 21.295 22.271 23.104 23.844 24.520 25.148 26.304 27.373 28.389 29.376 30.353
33 15.815 17.074 19.047 20.867 22.115 23.110 23.960 24.714 25.403 26.042 27.219 28.307 29.340 30.344 31.337
34 16.501 17.789 19.806 21.664 22.938 23.952 24.818 25.586 26.287 26.938 28.136 29.242 30.293 31.313 32.322
35 17.192 18.509 20.569 22.465 23.763 24.797 25.678 26.460 27.174 27.836 29.054 30.178 31.246 32.282 33.306
36 17.887 19.233 21.336 23.269 24.591 25.643 26.540 27.336 28.062 28.735 29.973 31.115 32.200 33.252 34.291
37 18.586 19.960 22.106 24.075 25.421 26.492 27.404 28.214 28.951 29.635 30.893 32.053 33.154 34.222 35.276
38 19.289 20.691 22.878 24.884 26.254 27.343 28.270 29.093 29.842 30.537 31.815 32.992 34.109 35.192 36.262
39 19.996 21.426 23.654 25.695 27.089 28.196 29.138 29.974 30.735 31.441 32.737 33.932 35.064 36.163 37.247
40 20.707 22.164 24.433 26.509 27.926 29.051 30.008 30.856 31.629 32.345 33.660 34.872 36.021 37.134 38.233
41 21.421 22.906 25.215 27.326 28.765 29.907 30.879 31.740 32.524 33.251 34.585 35.813 36.977 38.105 39.219
42 22.138 23.650 25.999 28.144 29.606 30.765 31.752 32.626 33.420 34.157 35.510 36.755 37.935 39.077 40.205
43 22.859 24.398 26.785 28.965 30.449 31.625 32.626 33.512 34.318 35.065 36.436 37.698 38.892 40.050 41.191
44 23.584 25.148 27.575 29.787 31.293 32.487 33.502 34.400 35.217 35.974 37.363 38.641 39.851 41.022 42.177
45 24.311 25.901 28.366 30.612 32.140 33.350 34.379 35.290 36.117 36.884 38.291 39.585 40.809 41.995 43.164
46 25.041 26.657 29.160 31.439 32.988 34.215 35.258 36.180 37.019 37.795 39.220 40.529 41.769 42.968 44.150
47 25.775 27.416 29.956 32.268 33.838 35.081 36.138 37.072 37.921 38.708 40.149 41.474 42.728 43.942 45.137
48 26.511 28.177 30.755 33.098 34.690 35.949 37.019 37.965 38.824 39.621 41.079 42.420 43.689 44.915 46.124
49 27.249 28.941 31.555 33.930 35.543 36.818 37.901 38.859 39.729 40.534 42.010 43.366 44.649 45.889 47.111
50 27.991 29.707 32.357 34.764 36.397 37.689 38.785 39.754 40.634 41.449 42.942 44.313 45.610 46.864 48.099
60 35.534 37.485 40.482 43.188 45.016 46.459 47.680 48.759 49.736 50.641 52.294 53.809 55.239 56.620 57.978
70 43.275 45.442 48.758 51.739 53.748 55.329 56.666 57.844 58.912 59.898 61.698 63.346 64.899 66.396 67.866
80 51.172 53.540 57.153 60.391 62.568 64.278 65.722 66.994 68.145 69.207 71.145 72.915 74.583 76.188 77.763
90 59.196 61.754 65.647 69.126 71.460 73.291 74.836 76.195 77.425 78.558 80.625 82.511 84.285 85.993 87.666
100 67.328 70.065 74.222 77.929 80.412 82.358 83.999 85.441 86.744 87.945 90.133 92.129 94.005 95.808 97.574
110 75.550 78.458 82.867 86.792 89.416 91.471 93.202 94.723 96.097 97.362 99.666 101.766 103.738 105.632 107.487
120 83.852 86.923 91.573 95.705 98.464 100.624 102.441 104.037 105.478 106.806 109.220 111.419 113.483 115.465 117.404
130 92.222 95.451 100.331 104.662 107.552 109.811 111.712 113.380 114.886 116.272 118.792 121.086 123.238 125.304 127.324
140 100.655 104.034 109.137 113.659 116.674 119.029 121.010 122.748 124.315 125.758 128.380 130.766 133.003 135.149 137.248
150 109.142 112.668 117.985 122.692 125.827 128.275 130.333 132.137 133.765 135.263 137.983 140.457 142.776 145.000 147.174
160 117.679 121.346 126.870 131.756 135.007 137.546 139.678 141.547 143.233 144.783 147.599 150.158 152.556 154.856 157.102
170 126.261 130.064 135.790 140.849 144.214 146.839 149.044 150.976 152.717 154.319 157.227 159.869 162.344 164.716 167.033
180 134.884 138.820 144.741 149.969 153.443 156.153 158.427 160.421 162.217 163.868 166.865 169.588 172.137 174.580 176.965
190 143.545 147.610 153.721 159.113 162.693 165.485 167.828 169.881 171.730 173.430 176.514 179.315 181.936 184.448 186.900
200 152.241 156.432 162.728 168.279 171.963 174.835 177.245 179.355 181.256 183.003 186.172 189.049 191.741 194.319 196.836
