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4Opción B

2,5 puntos

En la cuarta pregunta debe seleccionar sólo una opción (A o B) y contestar a todos sus apartados.

i
El importe de los préstamos que solicitan los jóvenes a los bancos para la compra de su primera vivienda sigue una distribución normal con desviación típica 4848 (en miles de euros). Se selecciona una muestra de jóvenes que solicitan un préstamo, obteniéndose los siguientes importes (en miles de euros): 160160 275275 300300 250250 280280 310310 180180 200200 y 223223. Calcule un intervalo de confianza al 95%95\% para el importe medio de este tipo de préstamos. (Utilice 22 decimales).1,5 pts
ii
Calcule ∫7x24x3−2 dx\displaystyle\int \dfrac{7x^2}{4x^3 - 2}\,dx.1 pt

Formulario

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Tabla de la distribución normal estándar Z∼N(0,1)Z \sim N(0,1) P(Z<k)=12π∫−∞ke−t2/2 dtP(Z < k) = \dfrac{1}{\sqrt{2\pi}}\displaystyle\int_{-\infty}^{k} e^{-t^2/2}\,dt
Densidad de la normal estándar y función de distribución, con el área hasta k sombreada 1 1 0,5 0,5 k k
kk01
−3,50,00020,0002
−3,40,00030,0003
−3,30,00050,0005
−3,20,00070,0007
−3,10,00100,0009
−3,00,00130,0013
−2,90,00190,0018
−2,80,00260,0025
−2,70,00350,0034
−2,60,00470,0045
−2,50,00620,0060
−2,40,00820,0080
−2,30,01070,0104
−2,20,01390,0136
−2,10,01790,0174
−2,00,02280,0222
−1,90,02870,0281
−1,80,03590,0351
−1,70,04460,0436
−1,60,05480,0537
−1,50,06680,0655
−1,40,08080,0793
−1,30,09680,0951
−1,20,11510,1131
−1,10,13570,1335
−1,00,15870,1562
−0,90,18410,1814
−0,80,21190,2090
−0,70,24200,2389
−0,60,27430,2709
−0,50,30850,3050
−0,40,34460,3409
−0,30,38210,3783
−0,20,42070,4168
−0,10,46020,4562
−0,00,50000,4960
kk01
0,00,50000,5040
0,10,53980,5438
0,20,57930,5832
0,30,61790,6217
0,40,65540,6591
0,50,69150,6950
0,60,72570,7291
0,70,75800,7611
0,80,78810,7910
0,90,81590,8186
1,00,84130,8438
1,10,86430,8665
1,20,88490,8869
1,30,90320,9049
1,40,91920,9207
1,50,93320,9345
1,60,94520,9463
1,70,95540,9564
1,80,96410,9649
1,90,97130,9719
2,00,97720,9778
2,10,98210,9826
2,20,98610,9864
2,30,98930,9896
2,40,99180,9920
2,50,99380,9940
2,60,99530,9955
2,70,99650,9966
2,80,99740,9975
2,90,99810,9982
3,00,99870,9987
3,10,99900,9991
3,20,99930,9993
3,30,99950,9995
3,40,99970,9997
3,50,99980,9998
kk23
−3,50,00020,0002
−3,40,00030,0003
−3,30,00050,0004
−3,20,00060,0006
−3,10,00090,0009
−3,00,00130,0012
−2,90,00180,0017
−2,80,00240,0023
−2,70,00330,0032
−2,60,00440,0043
−2,50,00590,0057
−2,40,00780,0075
−2,30,01020,0099
−2,20,01320,0129
−2,10,01700,0166
−2,00,02170,0212
−1,90,02740,0268
−1,80,03440,0336
−1,70,04270,0418
−1,60,05260,0516
−1,50,06430,0630
−1,40,07780,0764
−1,30,09340,0918
−1,20,11120,1093
−1,10,13140,1292
−1,00,15390,1515
−0,90,17880,1762
−0,80,20610,2033
−0,70,23580,2327
−0,60,26760,2643
−0,50,30150,2981
−0,40,33720,3336
−0,30,37450,3707
−0,20,41290,4090
−0,10,45220,4483
−0,00,49200,4880
kk23
0,00,50800,5120
0,10,54780,5517
0,20,58710,5910
0,30,62550,6293
0,40,66280,6664
0,50,69850,7019
0,60,73240,7357
0,70,76420,7673
0,80,79390,7967
0,90,82120,8238
1,00,84610,8485
1,10,86860,8708
1,20,88880,8907
1,30,90660,9082
1,40,92220,9236
1,50,93570,9370
1,60,94740,9484
1,70,95730,9582
1,80,96560,9664
1,90,97260,9732
2,00,97830,9788
2,10,98300,9834
2,20,98680,9871
2,30,98980,9901
2,40,99220,9925
2,50,99410,9943
2,60,99560,9957
2,70,99670,9968
2,80,99760,9977
2,90,99820,9983
3,00,99870,9988
3,10,99910,9991
3,20,99940,9994
3,30,99950,9996
3,40,99970,9997
3,50,99980,9998
kk45
−3,50,00020,0002
−3,40,00030,0003
−3,30,00040,0004
−3,20,00060,0006
−3,10,00080,0008
−3,00,00120,0011
−2,90,00160,0016
−2,80,00230,0022
−2,70,00310,0030
−2,60,00410,0040
−2,50,00550,0054
−2,40,00730,0071
−2,30,00960,0094
−2,20,01250,0122
−2,10,01620,0158
−2,00,02070,0202
−1,90,02620,0256
−1,80,03290,0322
−1,70,04090,0401
−1,60,05050,0495
−1,50,06180,0606
−1,40,07490,0735
−1,30,09010,0885
−1,20,10750,1056
−1,10,12710,1251
−1,00,14920,1469
−0,90,17360,1711
−0,80,20050,1977
−0,70,22960,2266
−0,60,26110,2578
−0,50,29460,2912
−0,40,33000,3264
−0,30,36690,3632
−0,20,40520,4013
−0,10,44430,4404
−0,00,48400,4801
kk45
0,00,51600,5199
0,10,55570,5596
0,20,59480,5987
0,30,63310,6368
0,40,67000,6736
0,50,70540,7088
0,60,73890,7422
0,70,77040,7734
0,80,79950,8023
0,90,82640,8289
1,00,85080,8531
1,10,87290,8749
1,20,89250,8944
1,30,90990,9115
1,40,92510,9265
1,50,93820,9394
1,60,94950,9505
1,70,95910,9599
1,80,96710,9678
1,90,97380,9744
2,00,97930,9798
2,10,98380,9842
2,20,98750,9878
2,30,99040,9906
2,40,99270,9929
2,50,99450,9946
2,60,99590,9960
2,70,99690,9970
2,80,99770,9978
2,90,99840,9984
3,00,99880,9989
3,10,99920,9992
3,20,99940,9994
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
kk67
−3,50,00020,0002
−3,40,00030,0003
−3,30,00040,0004
−3,20,00060,0005
−3,10,00080,0008
−3,00,00110,0011
−2,90,00150,0015
−2,80,00210,0021
−2,70,00290,0028
−2,60,00390,0038
−2,50,00520,0051
−2,40,00690,0068
−2,30,00910,0089
−2,20,01190,0116
−2,10,01540,0150
−2,00,01970,0192
−1,90,02500,0244
−1,80,03140,0307
−1,70,03920,0384
−1,60,04850,0475
−1,50,05940,0582
−1,40,07210,0708
−1,30,08690,0853
−1,20,10380,1020
−1,10,12300,1210
−1,00,14460,1423
−0,90,16850,1660
−0,80,19490,1922
−0,70,22360,2206
−0,60,25460,2514
−0,50,28770,2843
−0,40,32280,3192
−0,30,35940,3557
−0,20,39740,3936
−0,10,43640,4325
−0,00,47610,4721
kk67
0,00,52390,5279
0,10,56360,5675
0,20,60260,6064
0,30,64060,6443
0,40,67720,6808
0,50,71230,7157
0,60,74540,7486
0,70,77640,7794
0,80,80510,8078
0,90,83150,8340
1,00,85540,8577
1,10,87700,8790
1,20,89620,8980
1,30,91310,9147
1,40,92790,9292
1,50,94060,9418
1,60,95150,9525
1,70,96080,9616
1,80,96860,9693
1,90,97500,9756
2,00,98030,9808
2,10,98460,9850
2,20,98810,9884
2,30,99090,9911
2,40,99310,9932
2,50,99480,9949
2,60,99610,9962
2,70,99710,9972
2,80,99790,9979
2,90,99850,9985
3,00,99890,9989
3,10,99920,9992
3,20,99940,9995
3,30,99960,9996
3,40,99970,9997
3,50,99980,9998
kk89
−3,50,00020,0002
−3,40,00030,0002
−3,30,00040,0003
−3,20,00050,0005
−3,10,00070,0007
−3,00,00100,0010
−2,90,00140,0014
−2,80,00200,0019
−2,70,00270,0026
−2,60,00370,0036
−2,50,00490,0048
−2,40,00660,0064
−2,30,00870,0084
−2,20,01130,0110
−2,10,01460,0143
−2,00,01880,0183
−1,90,02390,0233
−1,80,03010,0294
−1,70,03750,0367
−1,60,04650,0455
−1,50,05710,0559
−1,40,06940,0681
−1,30,08380,0823
−1,20,10030,0985
−1,10,11900,1170
−1,00,14010,1379
−0,90,16350,1611
−0,80,18940,1867
−0,70,21770,2148
−0,60,24830,2451
−0,50,28100,2776
−0,40,31560,3121
−0,30,35200,3483
−0,20,38970,3859
−0,10,42860,4247
−0,00,46810,4641
kk89
0,00,53190,5359
0,10,57140,5753
0,20,61030,6141
0,30,64800,6517
0,40,68440,6879
0,50,71900,7224
0,60,75170,7549
0,70,78230,7852
0,80,81060,8133
0,90,83650,8389
1,00,85990,8621
1,10,88100,8830
1,20,89970,9015
1,30,91620,9177
1,40,93060,9319
1,50,94290,9441
1,60,95350,9545
1,70,96250,9633
1,80,96990,9706
1,90,97610,9767
2,00,98120,9817
2,10,98540,9857
2,20,98870,9890
2,30,99130,9916
2,40,99340,9936
2,50,99510,9952
2,60,99630,9964
2,70,99730,9974
2,80,99800,9981
2,90,99860,9986
3,00,99900,9990
3,10,99930,9993
3,20,99950,9995
3,30,99960,9997
3,40,99970,9998
3,50,99980,9998