v
0,001
0,005
0,01
0,02
0,025
0,03
0,04
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
v
1
10,828
7,879
6,635
5,412
5,024
4,709
4,218
3,841
2,706
2,072
1,642
1,323
1,074
0,873
0,708
1
2
13,816
10,597
9,210
7,824
7,378
7,013
6,438
5,991
4,605
3,794
3,219
2,773
2,408
2,100
1,833
2
3
16,266
12,838
11,345
9,837
9,348
8,947
8,311
7,815
6,251
5,317
4,642
4,108
3,665
3,283
2,946
3
4
18,467
14,860
13,277
11,668
11,143
10,712
10,026
9,488
7,779
6,745
5,989
5,385
4,878
4,438
4,045
4
5
20,515
16,750
15,086
13,388
12,833
12,375
11,644
11,070
9,236
8,115
7,289
6,626
6,064
5,573
5,132
5
6
22,458
18,548
16,812
15,033
14,449
13,968
13,198
12,592
10,645
9,446
8,558
7,841
7,231
6,695
6,211
6
7
24,322
20,278
18,475
16,622
16,013
15,509
14,703
14,067
12,017
10,748
9,803
9,037
8,383
7,806
7,283
7
8
26,124
21,955
20,090
18,168
17,535
17,010
16,171
15,507
13,362
12,027
11,030
10,219
9,524
8,909
8,351
8
9
27,877
23,589
21,666
19,679
19,023
18,480
17,608
16,919
14,684
13,288
12,242
11,389
10,656
10,006
9,414
9
10
29,588
25,188
23,209
21,161
20,483
19,922
19,021
18,307
15,987
14,534
13,442
12,549
11,781
11,097
10,473
10
11
31,264
26,757
24,725
22,618
21,920
21,342
20,412
19,675
17,275
15,767
14,631
13,701
12,899
12,184
11,530
11
12
32,909
28,300
26,217
24,054
23,337
22,742
21,785
21,026
18,549
16,989
15,812
14,845
14,011
13,266
12,584
12
13
34,528
29,819
27,688
25,472
24,736
24,125
23,142
22,362
19,812
18,202
16,985
15,984
15,119
14,345
13,636
13
14
36,123
31,319
29,141
26,873
26,119
25,493
24,485
23,685
21,064
19,406
18,151
17,117
16,222
15,421
14,685
14
15
37,697
32,801
30,578
28,259
27,488
26,848
25,816
24,996
22,307
20,603
19,311
18,245
17,322
16,494
15,733
15
16
39,252
34,267
32,000
29,633
28,845
28,191
27,136
26,296
23,542
21,793
20,465
19,369
18,418
17,565
16,780
16
17
40,790
35,718
33,409
30,995
30,191
29,523
28,445
27,587
24,769
22,977
21,615
20,489
19,511
18,633
17,824
17
18
42,312
37,156
34,805
32,346
31,526
30,845
29,745
28,869
25,989
24,155
22,760
21,605
20,601
19,699
18,868
18
19
43,820
38,582
36,191
33,687
32,852
32,158
31,037
30,144
27,204
25,329
23,900
22,718
21,689
20,764
19,910
19
20
45,315
39,997
37,566
35,020
34,170
33,462
32,321
31,410
28,412
26,498
25,038
23,828
22,775
21,826
20,951
20
21
46,797
41,401
38,932
36,343
35,479
34,759
33,597
32,671
29,615
27,662
26,171
24,935
23,858
22,888
21,991
21
22
48,268
42,796
40,289
37,659
36,781
36,049
34,867
33,924
30,813
28,822
27,301
26,039
24,939
23,947
23,031
22
23
49,728
44,181
41,638
38,968
38,076
37,332
36,131
35,172
32,007
29,979
28,429
27,141
26,018
25,006
24,069
23
24
51,179
45,559
42,980
40,270
39,364
38,609
37,389
36,415
33,196
31,132
29,553
28,241
27,096
26,063
25,106
24
25
52,620
46,928
44,314
41,566
40,646
39,880
38,642
37,652
34,382
32,282
30,675
29,339
28,172
27,118
26,143
25
26
54,052
48,290
45,642
42,856
41,923
41,146
39,889
38,885
35,563
33,429
31,795
30,435
29,246
28,173
27,179
26
27
55,476
49,645
46,963
44,140
43,195
42,407
41,132
40,113
36,741
34,574
32,912
31,528
30,319
29,227
28,214
27
28
56,892
50,993
48,278
45,419
44,461
43,662
42,370
41,337
37,916
35,715
34,027
32,620
31,391
30,279
29,249
28
29
58,301
52,336
49,588
46,693
45,722
44,913
43,604
42,557
39,087
36,854
35,139
33,711
32,461
31,331
30,283
29
30
59,703
53,672
50,892
47,962
46,979
46,160
44,834
43,773
40,256
37,990
36,250
34,800
33,530
32,382
31,316
30
31
61,098
55,003
52,191
49,226
48,232
47,402
46,059
44,985
41,422
39,124
37,359
35,887
34,598
33,431
32,349
31
32
62,487
56,328
53,486
50,487
49,480
48,641
47,282
46,194
42,585
40,256
38,466
36,973
35,665
34,480
33,381
32
33
63,870
57,648
54,776
51,743
50,725
49,876
48,500
47,400
43,745
41,386
39,572
38,058
36,731
35,529
34,413
33
34
65,247
58,964
56,061
52,995
51,966
51,107
49,716
48,602
44,903
42,514
40,676
39,141
37,795
36,576
35,444
34
35
66,619
60,275
57,342
54,244
53,203
52,335
50,928
49,802
46,059
43,640
41,778
40,223
38,859
37,623
36,475
35
40
73,402
66,766
63,691
60,436
59,342
58,428
56,946
55,758
51,805
49,244
47,269
45,616
44,165
42,848
41,622
40
60
99,607
91,952
88,379
84,580
83,298
82,225
80,482
79,082
74,397
71,341
68,972
66,981
65,227
63,628
62,135
60
80
124,839
116,321
112,329
108,069
106,629
105,422
103,459
101,879
96,578
93,106
90,405
88,130
86,120
84,284
82,566
80
90
137,208
128,299
124,116
119,648
118,136
116,869
114,806
113,145
107,565
103,904
101,054
98,650
96,524
94,581
92,761
90
100
149,449
140,169
135,807
131,142
129,561
128,237
126,079
124,342
118,498
114,659
111,667
109,141
106,906
104,862
102,946
100
120
173,617
163,648
158,950
153,918
152,211
150,780
148,447
146,567
140,233
136,062
132,806
130,055
127,616
125,383
123,289
120
140
197,451
186,847
181,840
176,471
174,648
173,118
170,624
168,613
161,827
157,352
153,854
150,894
148,269
145,863
143,604
140
UNIVERSIDAD DE LA SABANA
PROBABILIDAD Y ESTADÍSTICA
DISTRIBUCIÓN CHI - CUADRADO

v
0,450
0,500
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
0,975
0,98
0,99
0,995
v
1
0,571
0,455
0,357
0,275
0,206
0,148
0,102
0,064
0,036
0,016
0,004
0,001
0,001
0,000
0,000
1
2
1,597
1,386
1,196
1,022
0,862
0,713
0,575
0,446
0,325
0,211
0,103
0,051
0,040
0,020
0,010
2
3
2,643
2,366
2,109
1,869
1,642
1,424
1,213
1,005
0,798
0,584
0,352
0,216
0,185
0,115
0,072
3
4
3,687
3,357
3,047
2,753
2,470
2,195
1,923
1,649
1,366
1,064
0,711
0,484
0,429
0,297
0,207
4
5
4,728
4,351
3,996
3,655
3,325
3,000
2,675
2,343
1,994
1,610
1,145
0,831
0,752
0,554
0,412
5
6
5,765
5,348
4,952
4,570
4,197
3,828
3,455
3,070
2,661
2,204
1,635
1,237
1,134
0,872
0,676
6
7
6,800
6,346
5,913
5,493
5,082
4,671
4,255
3,822
3,358
2,833
2,167
1,690
1,564
1,239
0,989
7
8
7,833
7,344
6,877
6,423
5,975
5,527
5,071
4,594
4,078
3,490
2,733
2,180
2,032
1,646
1,344
8
9
8,863
8,343
7,843
7,357
6,876
6,393
5,899
5,380
4,817
4,168
3,325
2,700
2,532
2,088
1,735
9
10
9,892
9,342
8,812
8,295
7,783
7,267
6,737
6,179
5,570
4,865
3,940
3,247
3,059
2,558
2,156
10
11
10,920
10,341
9,783
9,237
8,695
8,148
7,584
6,989
6,336
5,578
4,575
3,816
3,609
3,053
2,603
11
12
11,946
11,340
10,755
10,182
9,612
9,034
8,438
7,807
7,114
6,304
5,226
4,404
4,178
3,571
3,074
12
13
12,972
12,340
11,729
11,129
10,532
9,926
9,299
8,634
7,901
7,042
5,892
5,009
4,765
4,107
3,565
13
14
13,996
13,339
12,703
12,078
11,455
10,821
10,165
9,467
8,696
7,790
6,571
5,629
5,368
4,660
4,075
14
15
15,020
14,339
13,679
13,030
12,381
11,721
11,037
10,307
9,499
8,547
7,261
6,262
5,985
5,229
4,601
15
16
16,042
15,338
14,655
13,983
13,310
12,624
11,912
11,152
10,309
9,312
7,962
6,908
6,614
5,812
5,142
16
17
17,065
16,338
15,633
14,937
14,241
13,531
12,792
12,002
11,125
10,085
8,672
7,564
7,255
6,408
5,697
17
18
18,086
17,338
16,611
15,893
15,174
14,440
13,675
12,857
11,946
10,865
9,390
8,231
7,906
7,015
6,265
18
19
19,107
18,338
17,589
16,850
16,109
15,352
14,562
13,716
12,773
11,651
10,117
8,907
8,567
7,633
6,844
19
20
20,127
19,337
18,569
17,809
17,046
16,266
15,452
14,578
13,604
12,443
10,851
9,591
9,237
8,260
7,434
20
21
21,147
20,337
19,548
18,768
17,984
17,182
16,344
15,445
14,439
13,240
11,591
10,283
9,915
8,897
8,034
21
22
22,166
21,337
20,529
19,729
18,924
18,101
17,240
16,314
15,279
14,041
12,338
10,982
10,600
9,542
8,643
22
23
23,185
22,337
21,510
20,690
19,866
19,021
18,137
17,187
16,122
14,848
13,091
11,689
11,293
10,196
9,260
23
24
24,204
23,337
22,491
21,652
20,808
19,943
19,037
18,062
16,969
15,659
13,848
12,401
11,992
10,856
9,886
24
25
25,222
24,337
23,472
22,616
21,752
20,867
19,939
18,940
17,818
16,473
14,611
13,120
12,697
11,524
10,520
25
26
26,240
25,336
24,454
23,579
22,697
21,792
20,843
19,820
18,671
17,292
15,379
13,844
13,409
12,198
11,160
26
27
27,257
26,336
25,437
24,544
23,644
22,719
21,749
20,703
19,527
18,114
16,151
14,573
14,125
12,879
11,808
27
28
28,274
27,336
26,419
25,509
24,591
23,647
22,657
21,588
20,386
18,939
16,928
15,308
14,847
13,565
12,461
28
29
29,291
28,336
27,402
26,475
25,539
24,577
23,567
22,475
21,247
19,768
17,708
16,047
15,574
14,256
13,121
29
30
30,307
29,336
28,386
27,442
26,488
25,508
24,478
23,364
22,110
20,599
18,493
16,791
16,306
14,953
13,787
30
31
31,323
30,336
29,369
28,409
27,438
26,440
25,390
24,255
22,976
21,434
19,281
17,539
17,042
15,655
14,458
31
32
32,339
31,336
30,353
29,376
28,389
27,373
26,304
25,148
23,844
22,271
20,072
18,291
17,783
16,362
15,134
32
33
33,355
32,336
31,337
30,344
29,340
28,307
27,219
26,042
24,714
23,110
20,867
19,047
18,527
17,074
15,815
33
34
34,371
33,336
32,322
31,313
30,293
29,242
28,136
26,938
25,586
23,952
21,664
19,806
19,275
17,789
16,501
34
35
35,386
34,336
33,306
32,282
31,246
30,178
29,054
27,836
26,460
24,797
22,465
20,569
20,027
18,509
17,192
35
40
40,459
39,335
38,233
37,134
36,021
34,872
33,660
32,345
30,856
29,051
26,509
24,433
23,838
22,164
20,707
40
60
60,713
59,335
57,978
56,620
55,239
53,809
52,294
50,641
48,759
46,459
43,188
40,482
39,699
37,485
35,534
60
80
80,927
79,334
77,763
76,188
74,583
72,915
71,145
69,207
66,994
64,278
60,391
57,153
56,213
53,540
51,172
80
90
91,023
89,334
87,666
85,993
84,285
82,511
80,625
78,558
76,195
73,291
69,126
65,647
64,635
61,754
59,196
90
100
101,115
99,334
97,574
95,808
94,005
92,129
90,133
87,945
85,441
82,358
77,929
74,222
73,142
70,065
67,328
100
120
121,285
119,334
117,404
115,465
113,483
111,419
109,220
106,806
104,037
100,624
95,705
91,573
90,367
86,923
83,852
120
140
141,441
139,334
137,248
135,149
133,003
130,766
128,380
125,758
122,748
119,029
113,659
109,137
107,815
104,034
100,655
140
UNIVERSIDAD DE LA SABANA
PROBABILIDAD Y ESTADÍSTICA
