Assume that a procedure yields a binomial distribution with n=6 trials and a probability of success of p=0.10. Use a binomial probability table to find the probability that the number of successes x is exactly 3.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Assume that a procedure yields a binomial distribution with n=6 trials and a
![Binomial Probabilities
01
.05
10
.20
.30
.40
.50
60
.70
80
.90
.95
.99
2
.980
.902
.810
.640
.490
.360
.250
.160
090
040
010
002
0+
2
1
020
.095
.180
.320
.420
.480
.500
480
420
320
.180
095
.020
1
0+
.002
.010
.040
.090
.160
.250
360
490
640
810
902
.980
2
3
970
857
729
.512
.343
216
.125
064
027
005
001
0+
0+
3
1
029
.135
243
.384
.441
.432
.375
268
.189
096
027
007
0+
1
2
0+
.007
.027
.096
.189
.288
375
432
441
384
243
.135
.029
2
3
0+
0+
.001
.008
.027
.064
.125
216
343
512
.729
857
.970
3
4
951
.815
.656
410
.240
.130
.062
026
008
002
0+
0+
0+
1
039
.171
.292
410
.412
.346
.250
.154
076
026
004
0+
0+
1
2
001
.014
.049
.154
.265
.346
.375
346
265
.154
049
014
.001
3
0+
0+
.004
.026
.076
.154
.250
346
412
410
292
.171
.039
3
4.
0+
0+
0+
.002
.008
.026
.062
.130
240
410
656
815
.961
4.
5
951
.774
.590
.326
.168
.078
.031
010
002
0+
0+
0+
0+
5
1
048
.204
.328
410
.360
.259
.156
077
028
006
0+
0+
0+
1
001
.021
.073
.205
.309
.346
.312
230
.132
051
005
001
0+
2
3
0+
.001
.008
.051
.132
230
312
346
309
205
073
021
.001
3
4
0+
0+
0+
.006
.028
.077
.156
259
360
410
328
204
.048
4.
0+
0+
0+
0+
.00e
.010
.031
078
.168
328
590
.774
.951
941
.735
.531
.262
.118
.047
.016
004
001
0+
0+
0+
0+
6
1
057
.232
.354
.393
.303
.187
.094
037
010
002
0+
0+
0+
1
2
001
.031
.098
246
.324
.311
.234
.138
060
015
001
0+
0+
2
3
0+
.002
015
082
.185
276
312
276
.185
082
015
002
0+
3
4
0+
0+
.001
.015
.060
.138
.234
311
324
246
095
031
.001
5
0+
0+
0+
.002
.010
.037
.094
.187
303
393
354
232
.057
5
6
0+
0+
0+
0+
.001
.004
.016
047
.118
262
531
.735
.941
7
932
.698
478
.210
.082
.c28
.008
002
0+
0+
0+
0+
0+
1
066
.257
372
.367
.247
.131
.055
017
004
0+
0+
0+
0+
1
2
002
.041
.124
275
.318
.261
.164
077
025
004
0+
0+
0+
2
3
0+
.004
.023
.115
.227
.290
273
194
097
029
003
0+
0+
3
0+
0+
.003
.029
097
194
.273
290
227
.115
023
004
0+
4
0+
0+
0+
.004
.025
.077
.164
261
318
275
.124
041
.002
5
6
0+
0+
0+
0+
.004
.017
.065
.131
247
367
372
257
.066
6
0+
0+
0+
0+
0+
.00e
.008
028
082
210
478
698
.932
7
8
923
.663
430
.168
.058
.017
.004
001
0+
0+
0+
0+
0+
8
1
075
.279
.383
.336
.198
.090
.031
008
001
0+
0+
0+
0+
1
2
.003
.051
149
294
.296
.209
.109
041
010
001
0+
0+
0+
3
0+
.005
.033
.147
.254
.279
.219
.124
047
009
0+
0+
0+
3
4
0+
0+
.005
.046
.136
.232
.273
232
.136
046
005
0+
0+
5
0+
0+
0+
.009
.047
124
.219
279
254
.147
033
005
0+
5
0+
0+
0+
.001
.010
.041
.109
209
296
294
.149
051
.003
6
0+
0+
0+
0+
.001
.008
.031
.090
.198
336
383
279
.075
7
8
0+
0+
0+
0+
0+
.001
.004
017
058
.168
430
.663
.923
01
.05
.10
.20
.30
.40
.50
60
70
80
.90
95
.99
NOTE 0+ represents a positive probebilty less than 0.0005.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5534fc6-b142-4cfc-8ed1-53ce39208227%2Fbce0982d-f04d-4264-886f-4964522064a2%2Fhao5dj_processed.png&w=3840&q=75)
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