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la cuevadel empollón
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1Opción A

3 puntos

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

En un festival de cine con tres sesiones se venden tres tipos de entradas: Estándar, Premium y VIP. En la sesión inaugural se vendieron 55 entradas Premium, 2020 Estándar y 2020 VIP, obteniéndose una recaudación de 1800 €1800\,\text{€}. En la sesión nocturna se vendieron 1010 VIP, 1010 Estándar y 55 Premium, recaudándose 1000 €1000\,\text{€}. El día de la proyección de clausura, el número de entradas Premium superó en 44 al resto de entradas, que fueron 1212 VIP y 44 Estándar, arrojando una recaudación de 1560 €1560\,\text{€}.
a
Calcule el precio de cada tipo de entrada y la recaudación total obtenida.2,25 pts
b
Determine el tipo de entrada con la que se obtuvo una mayor recaudación y el valor de dicha recaudación.0,75 pts

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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.