Ing. Dennis García Ocaña Univ. Roberto Gabriel Illanes M. Día del Segundo Examen Parcial
Control de la Calidad. IND-3226 “A”.
NOTA: Los datos para los ejercicios prácticos 2 y 3 se encuentran en hojas anexas, cada persona deberá elaborar la
presente práctica con la hoja de datos correspondientes al último digito de sus respectivos C.I.
PREGUNTAS TEORICAS. 1. ¿Cuáles son los pasos para elaborar las distintas graficas de control para atributos (p, np, c y u)? 2. ¿Cuáles son las ventajas y desventajas del muestreo?, y ¿Qué es el muestreo estratificado? 3. ¿Cuáles son los pasos para el muestreo de aceptación? EJERCICIOS PRACTICOS. 1. Determine los límites de control tentativos y los límites de control revisados para una gráfica u , con los datos de la tabla siguiente, de acabado superficial superficial en rollos de papel blanco. bla nco. Suponga que todos los puntos fuera de control tienen causas asignables. asign ables.
2.
3.
4.
Una máquina perforadora tiene que producir agujeros de un cierto diámetro en unas planchas. Los datos en la variable "Diámetro" corresponden a los datos agrupados en 5 muestras diarias recogidas durante 40 días (hay 200 observaciones observaciones en total). a) Representa la gráfica X , R . b) ¿Cuáles son los límites tentativos y la linea central?, Interpreta la gráfica si existe algún punto fuera de los límites de control calcular los limites l imites revisados. revisados. c) Determinar la capacidad del proceso e interpretar el resultado. Durante el mes de junio, se realizaron controles sobre el contenido de botes de pintura de 5 kg, considerándose considerándose defectuosos aquellos que pesaran menos de 4.975 4.97 5 Kg. donde: Nro.: número de botes inspeccionados cada día Nro. Def.: número de botes defectuosos defectuosos encontrados entre los inspeccionados in speccionados Día: día del mes de junio en que se llevaron a cabo las inspecciones a) Dibuja la gráfica p para este problema. b) Vuelva a dibujar la grafica p sabiendo que la proporción bajo control es 0 .05 c) ¿Cuáles son los límites tentativos y la línea central? Y si fuera el caso los limites revisados. d) ¿Existe algún punto fuera de los intervalos? ¿Qué día se produjo? ¿Cuál podría ser la causa? Con la norma ANSI/ASQ Z1.4, un inspector de Administración Administración de servicios generales, g enerales, necesita determinar planes de muestreo sencillo para la siguiente información:
Auxiliar: Univ. Roberto Gabriel Gabriel Illanes Mamani
5.
6.
Una empresa fabrica sellos de aceite y ve que el promedio de población es 49.15 mm (1.935 pulg), la desviación estándar poblacional es 0.51 mm (0.020 pulg), y que los datos tienen distribución normal. Si el diámetro interno del sello es menor que el límite inferior de especificación, de 47.80 mm, se reprocesa la parte. Sin embargo, si es mayor que el límite de especificación superior de 49.80 mm, el sello se desecha. a) ¿Qué porcentaje de los sellos se reprocesa? ¿Qué porcentaje se desecha? b) Por diversas razones se cambia el promedio de proceso a 48.50 mm. Con esta nueva media o centro de proceso, ¿qué porcentaje de los sellos se reprocesa? ¿Qué porcentaje se desecha? Si el reproceso es económicamente factible, ¿es una decisión correcta el cambio de centro de proceso? Determinar la capacidad del proceso de bolsas con corteza de ciprés, en kilogramos, para los datos de la tabla siguiente. También determine los coeficientes Cp y Cpk para un límite superior de tolerancia (USL) de 130 kg, y límite inferior de tolerancia (LSL) de 75 kg.
Vo.Bo. Ing. Dennis García Ocaña DOCENTE DE LA MATERIA
Univ. Roberto Gabriel Illanes Mamani AUXILIAR DE LA MATERIA
“Si no estás cometiendo ningún error, no estás innovando. Si estas cometiendo los mismos errores, no estás aprendiendo” Rick Warren
Auxiliar: Univ. Roberto Gabriel Illanes Mamani
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
0
Ejercicio 3 Mes: Junio
Diametros
x1
x2
x3
x4
x5
33,3478
29,3542
26,0752
36,5231
36,9427
27,1109
32,9958
27,2460
36,2794
27,1140
30,4659
35,3579
29,1953
29,8861
29,9181
Nro.
Unid. Def.
Día
1032
57
1
37,7498
1043
52
3
27,3623
36,5403
992
53
5
26,3630
21,7776
24,9762
1014
52
6
32,2216
28,3486
38,1549
29,1458
1001
44
8
31,1156
37,0151
27,9753
32,5632
29,2043
1013
53
9
34,2332
21,9200
36,4790
31,0813
31,2300
1033
52
10
32,4867
34,3394
30,3236
29,3761
27,7107
1052
52
12
22,9975
27,9677
25,6758
24,8604
26,0894
993
45
13
32,7894
35,7771
25,5019
31,8855
28,2128
1011
47
15
33,2459
23,3042
34,3673
25,5021
34,3284
1056
56
18
32,5454
32,1047
30,7696
27,6429
39,4906
950
51
19
35,2403
33,2323
32,1547
30,1654
30,9172
1013
63
22
31,3084
31,3015
28,3761
34,0237
28,9335
957
54
23
27,3080
32,1883
32,5019
32,5029
32,8067
970
178
24
29,4027
26,9477
32,1164
25,6183
28,0496
20,2039
28,4946
41,0052
36,9275
37,4499
31,8931
29,7400
37,0129
31,1309
34,4274
30,4678
34,4665
34,2600
38,4818
25,0897
27,6356
30,6556
32,8289
26,1640
27,3205
27,3812
39,1496
28,4380
27,8695
35,3637
25,6774
33,5603
32,5562
27,9308
31,5523
29,8091
25,5489
31,0554
30,5712
31,5722
31,5174
31,1832
31,6982
27,0918
23,1707
28,6786
30,3917
30,5657
27,1440
30,9114
28,0004
33,4133
23,6895
21,4833
32,7425
29,8561
32,1175
31,4258
27,6472
27,4528
29,3010
31,8838
37,5734
32,0294
25,9896
26,1709
30,0654
34,6072
30,2647
29,2575
35,1702
32,7419
30,4915
30,3295
25,7839
31,7636
27,2240
33,4254
31,5320
29,7138
35,1238
35,4494
31,0740
32,6740
31,1168
28,0091
27,7060
32,4999
29,9952
35,4931
25,5251
30,3537
25,8106
29,1797
30,7194
33,2306
32,4155
36,1427
34,0327
27,8319
30,1648
33,9923
31,7377
30,3163
36,5368
26,9752
32,6935
22,3315
32,9165
33,3009
29,6435
39,9527
31,8798
28,1620
30,9230
21,9646
39,4879
35,0974
31,4158
32,6865
34,3357
35,5057
32,5542
34,9782
27,9677
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
Ejercicio 3 Mes: Julio
Diametros
x1
x2
x3
x4
x5
27,7190
31,5062
33,8915
38,3763
29,8963
24,0056
29,6719
31,1580
30,3206
29,7986
34,1475
37,1651
32,2121
25,7244
30,3340
Nro.
1
Unid. Def.
Día
1016
46
1
25,5575
1035
58
3
26,2508
33,0033
961
187
4
24,1958
32,5430
32,0007
1040
48
6
26,7078
26,8650
36,7281
27,9310
976
64
8
36,3101
41,0627
27,9452
32,3745
27,7632
1029
49
9
28,6769
32,7121
39,7057
33,1606
26,9865
1025
47
10
33,1806
43,5156
32,7264
30,4210
33,7033
1022
52
12
26,8608
32,0267
29,2249
29,3657
29,0059
962
52
13
24,9475
33,6931
31,1200
33,4836
29,4007
972
44
15
32,6666
36,6928
30,7373
29,2210
24,9663
1011
45
18
24,4295
32,2858
35,9114
30,3019
31,2505
992
46
19
24,7978
30,9132
32,0732
27,8935
40,7611
959
45
22
27,5799
38,7278
35,2719
27,2581
31,1588
981
47
23
24,0457
29,5195
34,8094
28,9264
24,3088
980
38
24
32,2342
36,2302
31,0749
25,2466
30,9871
28,8906
30,9575
31,5452
30,9943
24,2569
24,8253
35,9741
32,5118
30,4098
30,5943
26,4463
36,3916
28,8024
29,8360
23,2277
26,0539
29,6804
31,0456
21,0097
32,8768
29,7135
35,1320
31,6421
28,9569
34,5671
20,3416
37,1314
27,9069
31,9970
36,2077
27,2226
28,7919
35,7502
32,4768
35,5345
24,4344
34,4485
27,4731
31,7168
26,9676
31,3186
32,8529
29,1572
30,8509
31,7707
32,3942
28,0895
27,3220
24,5868
33,6444
30,5887
31,8996
36,2617
32,3575
25,7037
29,5942
32,3583
29,2784
30,4755
30,8070
19,4601
28,6657
25,0969
32,9408
33,0515
30,1122
25,1831
35,2528
33,3950
24,8473
26,4948
30,3621
37,7675
30,6559
26,1882
28,9381
33,9777
34,6891
32,3012
33,1127
28,6897
27,1060
32,5547
29,6594
29,9747
25,3670
39,0523
28,5619
29,7102
32,0979
32,3202
31,5983
28,9910
29,4705
35,4571
30,9590
25,7443
36,9185
27,1865
31,9282
28,5965
34,4436
36,6030
31,9343
26,8517
33,5684
39,9505
29,5679
35,9410
33,0080
36,3132
34,2120
35,2246
28,6859
29,3324
25,5673
34,6479
32,8685
28,9939
26,7351
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
Ejercicio 3 Mes: Agosto
Diametros
x1
x2
x3
x4
x5
27,9569
26,4136
29,3301
33,0398
33,0328
30,9397
34,7148
28,5401
23,1484
27,6087
30,0511
33,8831
30,0831
35,2597
31,6778
Nro.
2
Unid. Def.
Día
968
49
1
27,2322
982
41
3
36,1481
32,7207
1044
59
5
32,3575
23,5606
25,7098
973
209
7
27,4633
34,5314
34,4381
33,5991
999
47
8
34,7644
34,8411
32,1370
25,5612
21,5076
1028
49
9
33,0849
35,5175
30,4178
31,5419
31,1388
978
54
10
19,4231
34,5194
30,6414
33,8609
27,0667
1032
55
12
31,1417
28,9467
32,1566
33,2732
26,9065
989
59
13
33,3044
31,6110
35,6593
30,1482
30,6074
1056
40
15
29,9675
34,7676
35,2229
26,2960
28,6526
961
55
18
33,4338
26,6390
26,5774
29,5523
33,8830
1014
54
19
33,0992
30,1943
32,4836
26,7879
29,5711
983
52
22
35,2238
28,6896
31,1113
23,3400
34,0540
1016
35
23
34,9260
37,0089
34,2869
26,3944
28,0986
979
54
24
33,8343
39,9179
30,7994
32,3534
30,2758
23,3818
35,8361
36,5371
32,2166
31,5944
26,0384
30,0084
31,2826
28,3393
34,4653
32,7409
33,9154
26,1317
30,2472
32,4818
26,1005
32,1060
37,5814
31,8297
28,8493
27,5731
29,5869
33,7633
31,7961
24,5129
32,7472
34,3825
34,2615
32,0302
27,2565
30,0802
33,4391
29,2255
39,3229
31,3267
34,2552
28,4678
35,3355
21,8911
26,0091
24,6358
30,2675
23,0505
32,3561
31,1657
31,9180
31,8886
36,3906
32,1596
34,4283
23,4641
35,6192
31,9935
33,6490
30,9798
24,2293
28,0064
25,5417
28,6766
30,6599
31,1751
30,6098
27,0851
34,5510
31,6249
29,4385
31,0727
32,8296
31,6875
34,8639
25,4786
37,9335
32,8838
34,3953
35,7937
28,8298
41,0485
27,9757
34,8551
25,8995
27,6699
39,7096
30,1877
36,2877
30,8217
26,4146
37,6471
37,5978
30,7426
32,3555
30,9944
35,3073
30,1521
36,2682
28,9439
24,0413
34,2785
32,1309
31,9121
39,9813
31,2540
28,0009
35,1951
25,2815
33,4238
21,8997
32,3271
35,5873
30,4012
26,5962
32,1160
33,9159
32,5516
28,9801
33,2475
31,3739
34,9137
25,5234
24,0834
32,8010
Los siguientes datos son para todos los que su número de carnet de identidad termina en: Ejercicio 2
3
Ejercicio 3 Mes: Septiembre
Diametros
x1
x2
x3
x4
x5
31,9751
29,3945
32,6352
37,7372
34,0234
26,5164
31,2630
23,7996
31,4781
30,3193
35,3748
17,8835
27,9135
21,0487
24,3446
Nro.
Unid. Def.
Día
1023
55
1
32,2367
983
44
3
33,6027
32,6838
957
40
5
32,1623
39,3202
35,7994
970
45
7
35,1716
25,9640
29,6431
29,8138
964
42
8
28,4628
28,4862
33,6322
33,9205
29,7949
939
31
9
28,1683
30,0101
36,3292
32,1759
32,9696
994
38
10
28,8341
33,5386
26,0836
27,6036
30,0928
967
30
12
28,7951
32,3298
34,0316
20,8646
27,0364
970
52
13
23,6456
23,5430
30,6340
21,4842
36,4813
961
39
15
34,3771
23,9853
27,6523
30,6149
31,9373
1007
52
18
35,2967
32,2943
36,2963
29,5563
26,7332
983
55
19
29,4941
26,3579
27,9334
30,3672
31,4215
959
193
22
27,0513
23,4749
34,9112
26,3376
32,4246
1024
41
23
30,8549
28,5634
36,3355
32,9085
23,6630
991
41
24
28,3979
28,4095
21,6442
32,8319
27,5698
30,2598
25,3548
41,7982
29,1211
25,7372
22,9680
25,5606
35,4245
35,0310
37,4337
36,7470
31,1627
34,2003
25,4275
32,4315
31,3096
22,3590
26,9313
27,7727
37,4510
32,8639
35,2591
29,9694
30,9934
35,2371
36,3946
32,6613
25,5126
26,8062
34,9135
21,7410
28,8995
25,9294
36,9330
30,2825
27,0255
29,9079
27,4202
37,9785
34,1399
30,7047
26,3681
33,3564
32,9438
27,6683
32,1114
25,8254
38,3705
26,3826
30,1041
27,7874
31,4941
36,3919
34,6352
30,3456
31,1931
33,6061
29,0350
21,7735
33,7938
25,0936
35,1142
22,2897
29,8602
25,8205
29,2413
29,4862
31,9480
44,8101
27,4493
28,7931
32,4513
28,0584
33,7568
34,7911
33,8278
37,8261
23,8823
27,4004
39,8773
27,8665
39,0653
32,7921
35,5471
35,4660
26,3957
28,5042
33,3249
30,8665
32,2289
26,4298
38,9522
34,4264
36,1413
33,8057
31,1149
29,3617
29,9349
30,5405
34,3108
27,0168
27,1869
29,3301
37,3679
41,8316
36,4139
32,2539
30,1768
36,0355
33,7086
32,2971
29,7988
30,3027
32,8555
37,7552
31,2826
34,6544
31,8703
30,8029
33,6816
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
4
Ejercicio 3 Mes: Noviembre
Diametros
x1
x2
x3
x4
x5
29,7088
30,7004
24,3424
33,9653
30,9904
26,0228
30,9177
28,7888
34,2479
27,0106
25,0364
27,7217
29,8767
32,8000
33,9534
Nro.
Unid. Def.
Día
941
61
2
33,8384
1030
200
3
30,4288
36,0192
1015
41
5
29,5140
30,6006
29,2072
984
42
7
31,7075
28,4393
27,7995
35,4526
1006
56
8
27,6039
35,8192
26,6229
32,9730
40,0420
996
53
9
35,9066
27,9593
23,0490
35,9503
33,3550
975
49
10
26,7448
29,9734
28,2019
36,1838
43,3823
977
41
12
32,5802
27,8980
23,8083
29,8872
30,2981
978
47
13
24,7603
32,8708
29,6169
31,8685
44,1472
1010
54
15
26,5303
34,3535
33,6309
34,5229
32,9327
1022
52
18
28,1031
32,0022
39,4784
29,8058
34,0866
1010
41
19
30,8897
41,0872
32,0791
32,9185
29,3436
978
48
22
37,4853
29,3588
31,6421
33,4212
25,1945
997
55
23
30,4401
31,7180
34,2103
34,0851
31,7303
984
55
24
28,3546
22,1327
31,7151
29,5361
35,3533
32,0450
27,8159
35,1804
37,3832
36,3160
25,2035
22,4464
29,2558
35,8997
26,3006
29,6146
29,5682
30,5229
22,4883
25,3108
31,7833
24,7354
27,3695
27,6307
31,2534
28,8167
27,3095
27,9629
30,6972
33,1799
29,3280
26,3905
28,6193
23,9511
42,6664
30,7182
29,3808
34,2496
38,2706
31,7604
31,6845
33,7890
31,2782
32,9333
33,7503
36,7107
36,2015
23,6653
34,5857
36,7908
37,9878
31,7162
38,3095
27,4824
30,8972
32,7879
27,7568
33,6163
32,7882
28,5376
24,5345
30,7172
24,8209
38,7875
26,6307
31,4522
26,9140
29,4996
34,9041
37,6994
27,7318
26,2264
31,8308
35,1701
34,9406
25,8234
24,3697
27,9375
34,4134
40,5819
32,7886
22,3755
30,5746
31,7664
32,1831
31,9361
29,7388
32,3551
27,5653
38,0351
29,2250
32,6886
35,1338
40,5769
42,1976
28,4876
30,8246
25,3807
26,5887
36,4081
26,4545
29,9675
26,8777
33,8281
34,0714
22,6392
30,0802
28,4265
33,5647
27,5583
23,4872
27,7662
31,6831
40,2921
38,9550
25,3048
37,5443
36,3794
30,7067
36,7343
28,3384
29,1201
38,7451
37,8725
30,8771
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
5
Ejercicio 3 Mes: Diciembre
Diametros
x1
x2
x3
x4
x5
33,2290
30,9818
21,5850
33,1630
38,4768
25,8902
24,3979
27,3413
33,7357
35,1780
33,8783
35,8004
30,0597
36,3748
30,8748
Nro.
Unid. Def.
Día
999
54
1
34,6675
1038
55
3
28,6398
33,2750
1004
56
5
28,6808
29,9557
34,1767
994
44
7
24,2483
40,8075
37,0683
34,8905
1012
62
8
36,8528
23,8631
23,4602
35,0290
40,1309
976
50
9
21,6848
29,7012
27,8547
32,2137
34,0423
976
40
10
30,4517
30,3258
32,1889
27,7317
39,0429
954
50
12
25,6540
26,6270
35,9704
29,0352
34,2679
1034
42
13
23,7668
27,7414
28,1790
34,4699
36,2139
1021
43
15
32,5496
29,8872
28,0143
33,4432
35,3235
1009
57
18
28,3817
25,0252
34,9410
31,6785
40,1143
1018
50
19
28,3867
32,9322
30,1637
34,9972
29,2477
993
56
22
30,3363
30,2383
32,9939
24,8321
29,3333
946
57
23
28,2586
30,5966
34,9231
36,8529
34,5040
1030
190
25
27,7495
36,3834
31,2196
31,7579
36,6391
33,5122
26,8910
34,3111
30,4299
33,6170
26,7414
36,2011
33,0606
34,4382
32,1909
28,9665
34,2200
24,7217
34,5743
38,9548
31,9732
29,3334
27,9632
36,0781
30,5134
26,7892
31,2579
33,2205
35,7377
36,2381
29,9667
35,6783
23,1695
36,9143
40,7152
32,5103
31,3094
27,9582
31,0021
34,5842
30,6175
31,9026
21,2245
29,1697
29,5544
40,3229
31,5950
28,3625
29,6247
42,7277
24,7750
29,7089
30,5409
30,9508
29,6379
34,0941
35,2591
32,2003
36,9714
34,1218
33,1112
33,9131
28,6640
25,8044
36,2817
26,6645
36,8885
18,7050
30,4530
37,9113
27,6533
28,3508
37,2042
33,1004
32,7457
30,2627
32,2605
29,3705
35,3046
36,5811
29,9506
32,9594
36,7124
28,0829
26,9147
29,6921
30,8806
25,5870
31,5828
34,2384
23,7657
35,2512
34,6159
32,5114
30,9593
36,8104
32,5166
33,1667
32,2502
27,2364
28,1241
25,5681
29,1399
33,4865
38,4147
30,3785
28,2120
40,7217
31,5841
39,8500
31,1483
27,0960
39,0819
29,2129
34,9449
33,6774
31,4162
34,1891
30,4527
29,6092
32,0405
27,9729
31,1240
32,0645
43,6609
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
6
Ejercicio 3 Mes: Enero
Diametros
x1
x2
x3
x4
x5
24,9967
29,9088
22,6486
26,1066
32,015
34,9509
30,4424
23,9908
32,2128
36,1127
33,2512
33,2768
37,1077
25,9636
32,5247
Unid. Def.
Día
1001
203
2
32,417
979
51
3
28,0796
28,324
986
41
5
29,0617
26,4257
32,912
993
39
7
25,9817
23,4736
25,3472
35,4731
1011
47
8
30,333
31,1318
28,7282
28,6327
40,4635
981
49
9
38,5602
31,159
26,8148
33,0756
33,3275
989
59
10
35,0539
29,0108
32,7632
25,0288
39,432
1032
44
12
22,9974
29,1245
29,832
30,6533
31,4773
1022
47
13
29,9423
33,5947
31,2962
30,9495
27,8016
1017
49
15
39,8724
27,4311
32,0258
30,6166
30,1042
1048
57
18
27,3234
29,2782
25,8856
35,9452
30,7401
1012
49
19
31,0397
32,8717
30,3977
34,573
35,4867
980
45
22
28,5107
31,2055
29,5346
43,6798
27,6581
1011
51
23
35,2742
36,1956
32,757
27,0057
32,5076
967
97
25
27,3877
29,823
37,5332
32,6285
28,5887
30,2487
29,8814
31,3017
35,1549
21,9873
27,0565
28,4716
29,6191
29,6917
34,0081
29,2827
27,7843
30,1247
34,1105
29,5674
34,3387
33,7294
27,5448
38,6868
37,5415
30,5477
24,7366
24,075
35,2003
31,8084
29,9376
28,7939
32,9151
35,5351
37,6173
26,246
19,6016
29,2087
31,1033
37,1843
24,0877
33,1203
32,5473
33,188
41,5075
31,4477
32,4118
31,2118
29,916
30,3769
31,9112
33,7712
29,0557
31,3786
28,4305
31,287
25,9043
31,9779
31,606
36,7962
22,4897
29,7287
33,8732
35,9887
31,3816
32,7221
30,327
31,6139
33,7379
31,4627
30,9336
22,9319
31,5351
31,8971
34,9281
34,958
22,8749
26,9752
30,4803
35,7751
30,5026
27,3586
36,2259
31,0304
35,5244
30,7189
35,4057
35,7965
27,3395
38,4094
27,5798
38,5455
20,6907
35,0264
37,4258
25,8526
30,6671
22,6549
36,6566
29,286
28,8189
23,1791
32,5445
27,9062
35,6079
35,8245
31,1061
27,5559
38,8064
31,6631
37,2101
31,578
26,0768
30,0233
30,0821
24,6655
29,6058
41,5662
32,6909
31,549
30,7058
27,3824
34,4604 33,4162 34,2739
Nro.
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
7
Ejercicio 3 Mes: Febrero
Diametros
x1
x2
x3
x4
x5
33,4732
33,4675
33,6201
21,7507
29,7900
26,7808
39,7263
35,8329
36,5229
26,9892
30,4408
25,5281
27,0168
30,1058
28,7614
Nro.
Unid. Def.
Día
1045
46
2
31,1728
1059
55
3
36,5628
33,7754
1061
41
5
37,2532
29,1844
36,5581
1038
48
7
33,8813
30,6030
28,4868
26,6333
944
54
8
23,9124
29,9790
28,8680
35,0929
31,7121
1020
48
9
33,3061
35,6382
36,6005
29,0436
30,1848
1079
183
11
27,5481
37,0314
32,6655
29,3904
30,0229
1014
64
12
33,8389
33,5400
28,6146
36,5987
34,4851
960
56
13
37,8920
34,5634
28,9438
32,1222
38,7491
946
57
15
31,1798
31,6129
27,4226
39,5235
34,8397
993
40
18
28,4294
30,7640
26,3778
28,8013
35,6430
1009
47
19
32,3037
27,2255
32,8667
29,7572
37,4975
971
46
22
25,4343
30,0441
29,9707
38,8355
36,9176
950
44
23
30,2443
25,5777
18,7408
29,4208
27,7343
1042
57
25
30,0493
37,6319
29,4018
26,3100
32,9072
29,3275
29,3384
32,3100
28,9763
33,5382
27,2506
27,0703
33,0125
32,6301
42,6325
26,0374
26,0370
29,3321
33,5134
36,6068
29,8010
33,5772
27,6727
32,7147
33,3047
32,8772
31,7929
32,4630
29,5889
34,4470
28,8677
33,5569
28,8043
28,0264
24,7653
24,3001
34,2933
33,3149
36,7558
23,6719
31,8462
29,5811
23,1768
41,5520
31,5164
34,3659
36,1893
33,0880
41,0621
38,1427
25,8228
30,6793
37,4045
41,2043
35,2282
18,6289
33,2162
33,9302
30,9197
32,2791
33,9873
23,1039
33,2230
34,0113
32,8573
30,3061
30,6965
27,7466
31,5232
40,7376
22,5331
28,0637
28,8441
31,9924
38,2223
27,5455
27,0735
36,2315
30,2694
32,5769
34,6774
21,4724
29,0697
31,2207
32,6893
27,6999
22,7585
23,9902
35,9414
34,3323
28,9408
29,7906
27,2937
33,8744
35,7335
30,0189
29,6552
34,6898
26,5404
29,1079
29,8424
25,2410
31,1640
33,0948
23,0562
27,9784
26,9834
32,6546
42,5867
31,8599
25,3687
33,7891
33,3890
31,7850
42,8360
32,8417
29,2695
38,6971
33,8900
31,5771
32,9127
29,7349
33,8565
23,6799
39,7406
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
8
Ejercicio 3 Mes: Marzo
Diametros
x1
x2
x3
x4
x5
34,5748
28,3253
31,9130
32,8484
29,7410
33,9161
35,6595
37,0987
36,1539
31,9703
26,6104
28,1178
35,0314
30,6645
32,3764
Nro.
Unid. Def.
Día
1000
50
2
36,9599
1025
53
3
27,1756
25,8732
1005
54
5
26,2989
35,7829
32,8239
1042
49
7
29,8072
30,0062
29,3777
36,5608
1025
53
8
31,8180
18,0911
32,5492
28,5865
31,1755
989
51
9
24,3286
34,0280
23,7242
38,3345
25,3852
976
52
11
26,3204
33,5375
32,8007
27,1389
31,4316
1035
58
12
24,2074
28,3765
33,8950
29,4122
28,5720
1005
63
13
24,0750
19,5233
29,7181
31,3593
40,0299
992
51
15
30,3892
26,1256
29,8653
33,0558
30,1232
1013
49
18
29,0950
32,2213
31,2099
33,1687
32,1203
1034
52
19
28,7311
33,0378
27,3735
35,1270
35,3001
975
219
20
32,5361
27,7118
29,7912
33,6160
33,6806
1011
49
24
30,1558
34,6322
33,0927
30,6983
31,0169
999
51
25
29,9343
28,7680
28,7206
30,5046
37,8107
31,7981
30,0127
25,5176
30,8229
32,5518
27,9107
24,3758
35,8425
25,1284
35,2513
25,7796
36,4964
31,6362
31,7843
32,8774
29,8087
30,5585
34,5303
32,8714
27,7086
28,0039
22,7334
33,2801
40,6929
28,6680
36,5099
18,8434
27,3291
34,2897
33,6301
29,0440
31,0497
37,8038
35,2601
27,1344
26,1533
30,4769
30,9008
27,6846
35,6942
29,3891
31,3292
27,9209
29,6804
34,4501
36,7321
28,2138
27,6499
24,4971
35,4261
36,2206
30,0210
30,6330
35,6700
33,2968
25,7991
29,1757
33,5205
29,8122
37,3221
30,3870
30,1982
32,5382
29,5796
30,3503
31,0065
33,7038
28,5604
32,1011
34,9016
38,9889
31,4031
29,3453
33,0460
38,9771
31,2418
26,8170
35,4724
34,9740
34,1186
37,9663
27,5110
28,1987
31,3520
36,7668
29,5230
35,7195
29,5997
33,7428
31,2576
28,9091
21,6604
38,2671
35,4451
33,8275
35,7778
30,1348
24,4396
32,2563
27,8094
29,7023
29,9373
32,1082
25,0910
29,7128
28,5499
27,7828
28,3019
34,8642
33,1156
26,8919
25,3456
31,8156
32,1465
27,2969
28,9995
30,4001
36,2295
31,2605
27,2074
Los siguientes datos son para todos los que su número de carnet de identidad termina en:
Ejercicio 2
9
Ejercicio 3 Mes: Mayo
Diametros
x1
x2
x3
x4
x5
28,6653
31,2312
21,8717
33,1584
30,7154
26,5690
28,0543
34,8810
28,2328
26,9137
28,6759
28,5409
35,8574
33,1068
34,3674
Nro.
Unid. Def.
Día
1027
69
2
27,3336
1029
52
3
35,3363
28,7722
1016
55
5
27,4690
33,5175
40,0666
945
48
7
28,6693
29,1098
27,9758
41,4311
1006
61
8
29,1328
38,3854
30,7223
31,9553
28,9099
1009
45
9
35,6797
31,5551
33,5884
26,1869
32,5516
1032
46
11
32,5074
27,3899
25,0780
29,7671
33,2516
1016
38
12
38,8861
29,7729
30,5015
24,8483
31,2428
1033
58
13
24,8304
31,6901
33,2295
28,5190
40,3401
985
44
16
34,6813
29,7005
25,7386
31,1406
35,2397
1014
49
18
25,2846
33,1468
21,9635
36,3279
30,5202
987
50
19
27,7284
29,4517
30,9727
31,3160
28,0123
1008
50
22
34,7092
32,5459
30,5979
28,7588
33,3806
1021
54
26
30,9028
36,3123
40,4312
31,9771
33,2656
1020
217
28
33,0304
29,8764
29,7871
27,3483
27,5111
26,6065
31,2653
29,9412
29,4118
35,7002
37,4381
37,9391
27,9331
38,2891
33,2266
29,8562
27,4198
34,8293
32,5208
38,2928
40,3661
31,2531
30,4432
28,7830
32,0700
27,2349
36,3695
37,7739
31,5903
35,0602
23,6939
26,1073
32,8292
29,3297
30,3920
27,5595
25,4090
35,2685
29,1773
33,0562
31,5068
24,0620
30,4897
31,1196
37,8518
35,0913
26,1356
31,7522
30,1974
38,6436
27,6329
29,8414
29,1870
32,5634
33,3461
38,9984
21,5122
28,5196
38,3254
43,1814
29,9347
22,6543
23,2986
30,8118
32,6569
32,9430
23,8319
25,2981
30,5950
38,1473
27,4366
29,0584
32,0720
35,4902
33,9906
35,7774
34,7977
29,5495
35,2849
32,6719
25,3640
29,8673
27,0637
34,3891
41,3767
32,7452
27,8345
36,4600
32,1586
35,1483
32,9216
29,7303
34,4678
27,4940
32,9230
32,0580
39,0240
29,2842
34,7297
33,2711
36,7833
30,8495
34,8871
30,9124
35,3088
27,2947
30,7536
26,4262
32,6562
33,9747
43,6510
31,1390
39,1906
30,1067
34,2575
28,4210
23,8817
31,0312
33,8071
33,3266
34,8235
20,5191
33,9870
30,9157
30,1531
