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3Opción A

2 puntos

Elija solo uno de los apartados A) o B):

a
Dada la población {−5−2131820}\{-5\quad -2\quad 13\quad 18\quad 20\}, se consideran todas las muestras de tamaño 33 obtenidas mediante muestreo aleatorio simple. Calcule la media y la varianza de la distribución de la variable media muestral.1 pt
b
Dados dos sucesos AA y BB de un mismo espacio muestral, se sabe que P(A)=0,75P(A)=0{,}75, P(Bc)=0,8P(B^c)=0{,}8 y P(A/B)=0,6P(A/B)=0{,}6. Calcule las siguientes probabilidades:P(A∩B)P(B−A)P(A∪B)P(Ac−B)\begin{gathered}P(A\cap B)\qquad P(B-A)\\P(A\cup B)\qquad P(A^c-B)\end{gathered}1 pt

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FUNCIÓN DE DISTRIBUCIÓN NORMAL N(0,1)N(0,1)
Distribución normal N(0, 1), con el área de probabilidad hasta z sombreada, el eje vertical en 0 y las marcas menos infinito, 0, z y más infinito.
zz0,000,010,02
0,00,50000,50400,5080
0,10,53980,54380,5478
0,20,57930,58320,5871
0,30,61790,62170,6255
0,40,65540,65910,6628
0,50,69150,69500,6985
0,60,72570,72910,7324
0,70,75800,76110,7642
0,80,78810,79100,7939
0,90,81590,81860,8212
1,00,84130,84380,8461
1,10,86430,86650,8686
1,20,88490,88690,8888
1,30,90320,90490,9066
1,40,91920,92070,9222
1,50,93320,93450,9357
1,60,94520,94630,9474
1,70,95540,95640,9573
1,80,96410,96490,9656
1,90,97130,97190,9726
2,00,97720,97780,9783
2,10,98210,98260,9830
2,20,98610,98640,9868
2,30,98930,98960,9898
2,40,99180,99200,9922
2,50,99380,99400,9941
2,60,99530,99550,9956
2,70,996530,996640,99674
2,80,997440,997520,99760
2,90,998130,998190,99825
3,00,998650,998690,99874
3,10,999030,999060,99910
3,20,999310,999340,99936
3,30,999520,999530,99955
3,40,999660,999680,99969
3,50,999770,999780,99978
3,60,999840,999850,99985
3,70,999890,999900,99990
3,80,999930,999930,99993
3,90,999950,999950,99996
4,00,999970,999970,99997
zz0,030,040,05
0,00,51200,51600,5199
0,10,55170,55570,5596
0,20,59100,59480,5987
0,30,62930,63310,6368
0,40,66640,67000,6736
0,50,70190,70540,7088
0,60,73570,73890,7422
0,70,76730,77040,7734
0,80,79670,79950,8023
0,90,82380,82640,8289
1,00,84850,85080,8531
1,10,87080,87290,8749
1,20,89070,89250,8944
1,30,90820,90990,9115
1,40,92360,92510,9265
1,50,93700,93820,9394
1,60,94840,94950,9505
1,70,95820,95910,9599
1,80,96640,96710,9678
1,90,97320,97380,9744
2,00,97880,97930,9798
2,10,98340,98380,9842
2,20,98710,98750,9878
2,30,99010,99040,9906
2,40,99250,99270,9929
2,50,99430,99450,9946
2,60,99570,99590,9960
2,70,996830,996930,99702
2,80,997670,997740,99781
2,90,998310,998360,99841
3,00,998780,998820,99886
3,10,999130,999160,99918
3,20,999380,999400,99942
3,30,999570,999580,99960
3,40,999700,999710,99972
3,50,999790,999800,99981
3,60,999860,999860,99987
3,70,999900,999910,99991
3,80,999940,999940,99994
3,90,999960,999960,99996
4,00,999970,999970,99997
zz0,060,070,08
0,00,52390,52790,5319
0,10,56360,56750,5714
0,20,60260,60640,6103
0,30,64060,64430,6480
0,40,67720,68080,6844
0,50,71230,71570,7190
0,60,74540,74860,7517
0,70,77640,77940,7823
0,80,80510,80780,8106
0,90,83150,83400,8365
1,00,85540,85770,8599
1,10,87700,87900,8810
1,20,89620,89800,8997
1,30,91310,91470,9162
1,40,92790,92920,9306
1,50,94060,94180,9429
1,60,95150,95250,9535
1,70,96080,96160,9625
1,80,96860,96930,9699
1,90,97500,97560,9761
2,00,98030,98080,9812
2,10,98460,98500,9854
2,20,98810,98840,9887
2,30,99090,99110,9913
2,40,99310,99320,9934
2,50,99480,99490,9951
2,60,99610,99620,9963
2,70,997110,997200,99728
2,80,997880,997950,99801
2,90,998460,998510,99856
3,00,998890,998930,99896
3,10,999210,999240,99926
3,20,999440,999460,99948
3,30,999610,999620,99964
3,40,999730,999740,99975
3,50,999810,999820,99983
3,60,999870,999880,99988
3,70,999920,999920,99992
3,80,999940,999950,99995
3,90,999960,999960,99997
4,00,999980,999980,99998
zz0,09
0,00,5359
0,10,5753
0,20,6141
0,30,6517
0,40,6879
0,50,7224
0,60,7549
0,70,7852
0,80,8133
0,90,8389
1,00,8621
1,10,8830
1,20,9015
1,30,9177
1,40,9319
1,50,9441
1,60,9545
1,70,9633
1,80,9706
1,90,9767
2,00,9817
2,10,9857
2,20,9890
2,30,9916
2,40,9936
2,50,9952
2,60,9964
2,70,99736
2,80,99807
2,90,99861
3,00,99900
3,10,99929
3,20,99950
3,30,99965
3,40,99976
3,50,99983
3,60,99989
3,70,99992
3,80,99995
3,90,99997
4,00,99998
Nota: En el interior de la tabla se da la probabilidad de que la variable aleatoria ZZ, con distribución N(0,1)N(0,1), esté por debajo del valor zz.