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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.

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.
Transcribed Image Text: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.
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