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A2

2 puntos
Apartado A
Tras varias denuncias presentadas por falta de peso en los paquetes de tomate frito, una organización de consumidores ha procedido a tomar una muestra de 6464 paquetes, resultando que la media de los pesos ha sido de 235 g235\,\text{g}. Asumiendo que el peso de los paquetes se ajusta a distribución normal con desviación típica 16 g16\,\text{g}, se pide:
a
Hallar un intervalo de confianza al 90%90\% para estimar el peso medio real de los paquetes de tomate frito de esa fábrica.1,25 pts
b
A la vista del intervalo obtenido y teniendo en cuenta que el peso que marca el paquete es de 250 g250\,\text{g}, ¿se puede decir que la denuncia tiene base?0,75 pts

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ANEXO TABLA DISTRIBUCIÓN NORMAL Tabla de distribución normal N(0,1)N(0, 1) F(z)=P(Z≤z)F(z) = P(Z \leq z)
Área acumulada de la distribución normal tipificada Campana simétrica respecto a cero. El área F(z) se extiende desde menos infinito hasta z, situado a la derecha de cero. F(z) 0 z −∞ +∞
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
2,70,99650,99660,9967
2,80,99740,99750,9976
2,90,99810,99820,9982
3,00,99870,99870,9987
3,10,99900,99910,9991
3,20,99930,99930,9994
3,30,99950,99950,9995
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99980,99980,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
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
2,70,99680,99690,9970
2,80,99770,99770,9978
2,90,99830,99840,9984
3,00,99880,99880,9989
3,10,99910,99920,9992
3,20,99940,99940,9994
3,30,99960,99960,9996
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99990,99990,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
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
2,70,99710,99720,9973
2,80,99790,99790,9980
2,90,99850,99850,9986
3,00,99890,99890,9990
3,10,99920,99920,9993
3,20,99940,99950,9995
3,30,99960,99960,9996
3,40,99970,99970,9997
3,50,99980,99980,9998
3,60,99990,99990,9999
3,70,99990,99990,9999
3,80,99990,99990,9999
3,91,00001,00001,0000
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
2,70,9974
2,80,9981
2,90,9986
3,00,9990
3,10,9993
3,20,9995
3,30,9997
3,40,9998
3,50,9998
3,60,9999
3,70,9999
3,80,9999
3,91,0000