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4.2

2,5 puntos
Bloque con optatividad 2

Resuelve sólo uno de los siguientes ejercicios:

Las tallas de las niñas al nacer se distribuyen según una distribución normal de media 50 cm50\,\text{cm} y desviación típica 1,8 cm1{,}8\,\text{cm}.
a
Halla la probabilidad de que una niña al nacer mida más de 54 cm54\,\text{cm}.1 pt
b
Si en un hospital durante un mes han nacido 100100 niñas, ¿cuántas tendrán en el momento del nacimiento una talla entre 48,248{,}2 y 51,8 cm51{,}8\,\text{cm}?1,5 pts

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FUNCIÓN DE DISTRIBUCIÓN NORMAL N(0,1)\mathrm{N}(0,1)
Distribución normal N(0,1) Área P(Z ≤ z) bajo la curva normal desde menos infinito hasta z. N(0,1) P(Z ≤ z) −∞ 0 z +∞
zz0,000,01
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
2,70,996530,99664
2,80,997440,99752
2,90,998130,99819
3,00,998650,99869
3,10,999030,99906
3,20,999310,99934
3,30,999520,99953
3,40,999660,99968
3,50,999770,99978
3,60,999840,99985
3,70,999890,99990
3,80,999930,99993
3,90,999950,99995
4,00,999970,99997
zz0,020,03
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
2,70,996740,99683
2,80,997600,99767
2,90,998250,99831
3,00,998740,99878
3,10,999100,99913
3,20,999360,99938
3,30,999550,99957
3,40,999690,99970
3,50,999780,99979
3,60,999850,99986
3,70,999900,99990
3,80,999930,99994
3,90,999960,99996
4,00,999970,99997
zz0,040,05
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
2,70,996930,99702
2,80,997740,99781
2,90,998360,99841
3,00,998820,99886
3,10,999160,99918
3,20,999400,99942
3,30,999580,99960
3,40,999710,99972
3,50,999800,99981
3,60,999860,99987
3,70,999910,99991
3,80,999940,99994
3,90,999960,99996
4,00,999970,99997
zz0,060,07
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
2,70,997110,99720
2,80,997880,99795
2,90,998460,99851
3,00,998890,99893
3,10,999210,99924
3,20,999440,99946
3,30,999610,99962
3,40,999730,99974
3,50,999810,99982
3,60,999870,99988
3,70,999920,99992
3,80,999940,99995
3,90,999960,99996
4,00,999980,99998
zz0,080,09
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
2,70,997280,99736
2,80,998010,99807
2,90,998560,99861
3,00,998960,99900
3,10,999260,99929
3,20,999480,99950
3,30,999640,99965
3,40,999750,99976
3,50,999830,99983
3,60,999880,99989
3,70,999920,99992
3,80,999950,99995
3,90,999970,99997
4,00,999980,99998
Nota: En el interior de la tabla se da la probabilidad de que la variable aleatoria ZZ, con distribución N(0,1)\mathrm{N}(0,1), esté por debajo del valor zz.