Problemas para la distribución normal helena preciado
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Publicado: 1 de octubre de 2010
Problemas para la distribución normal
Instrucciones: Resuelve el siguiente caso.
El tiempo de vida útil de un modelo de focos tiene una distribución de probabilidad normal con una media de 750 horas y una desviación típica de 40 horas.
a) Encuentra la probabilidad de que un foco dure 800 horas.
Utilizando la distribución normal tipificada, encuentra la probabilidad de que unabombilla dure menos de 784 horas.
Se sabe que la duración, en horas, de un foco de 75 watts tiene una distribución aproximadamente normal, con una desviación estándar de = 25 horas. Se toma una muestra aleatoria de 20 focos, la cual resulta tener una duración promedio de x = 1014 horas.
Construya un intervalo de confianza bilateral del 95% para la duración promedio.
|Distribución normalestándar |
Z | .00 | .01 |.02 |.03 |.04 | .05 |.06 |.07 |.08 |.09 | | 0.0 |0.00000 |0.00399 |0.00798 |0.01197 |0.01595 |0.01994 |0.02392 |0.02790 |0.03188 |0.03586 | | 0.1 |0.03983 |0.04380 |0.04776 |0.05172 |0.05567 |0.05962 |0.06356 |0.06749 |0.07142 |0.07535 | | 0.2 |0.07926|0.08317 |0.08706 |0.09095 |0.09483 |0.09871 |0.10257 |0.10642 |0.11026 |0.11409 | | 0.3 |0.11791 |0.12172 |0.12552 |0.12930 |0.13307 |0.13683 |0.14058 |0.14431 |0.14803 |0.15173 | | 0.4 |0.15542 |0.15910 |0.16276 |0.16640 |0.17003 |0.17364 |0.17724 |0.18082 |0.18439 |0.18793 | | 0.5 |0.19146 |0.19497 |0.19847 |0.20194 |0.20540 |0.20884 |0.21226 |0.21566 |0.21904 |0.22240 | | 0.6 |0.22575 |0.22907|0.23237 |0.23565 |0.23891 |0.24215 |0.24537 |0.24857 |0.25175 |0.25490 | | 0.7 |0.25804 |0.26115 |0.26424 |0.26730 |0.27035 |0.27337 |0.27637 |0.27935 | 0.28230 |0.28524 | | 0.8 |0.28814 |0.29103 |0.29389 |0.29673 |0.29955 |0.30234 |0.30511 |0.30785 |0.31057 |0.31327 | | 0.9 |0.31594 |0.31859 |0.32121 |0.32381 |0.32639 |0.32894 |0.33147 |0.33398 |0.33646 |0.33891 | | 1.0 |0.34134 |0.34375 |0.34614|0.34849 |0.35083 |0.35314 |0.35543 |0.35769 |0.35993 |0.36214 | | 1.1 |0.36433 |0.36650 |0.36864 |0.37076 | 0.37286 |0.37493 |0.37698 |0.37900 |0.38100 |0.38298 | | 1.2 |0.38493 |0.38686 |0.38877 |0.39065 |0.39251 | 0.39435 |0.39617 |0.39796 |0.39973 |0.40147 | | 1.3 |0.40320 |0.40490 |0.40658 |0.40824 |0.40988 |0.41149 |0.41308 |0.41466 |0.41621 |0.41774 | | 1.4 |0.41924 |0.42073 |0.42220|0.42364 |0.42507 |0.42647 |0.42785 |0.42922 |0.43056 |0.43189 | | 1.5 |0.43319 |0.43448 |0.43574 |0.43699 |0.43822 |0.43943 |0.44062 |0.44179 |0.44295 |0.44408 | | 1.6 |0.44520 |0.44630 |0.44738 |0.44845 |0.44950 |0.45053 |0.45154 |0.45254 |0.45352 |0.45449 | | 1.7 |0.45543 |0.45637 |0.45728 |0.45818 |0.45907 |0.45994 |0.46080 |0.46164 |0.46246 |0.46327 | | 1.8 |0.46407 |0.46485 |0.46562 |0.46638|0.46712 |0.46784 |0.46856 |0.46926 |0.46995 |0.47062 | | 1.9 |0.47128 |0.47193 |0.47257 |0.47320 |0.47381 |0.47441 |0.47500 |0.47558 |0.47615 |0.47670 | | 2.0 |0.47725 |0.47778 |0.47831 |0.47882 |0.47932 |0.47982 |0.48030 |0.48077 |0.48124 |0.48169 | | 2.1 |0.48214 |0.48257 |0.48300 |0.48341 |0.48382 |0.48422 |0.48461 |0.48500 |0.48537 |0.48574 | | 2.2 |0.48610 |0.48645 |0.48679 |0.48713 |0.48745|0.48778 |0.48809 |0.48840 |0.48870 |0.48899 | | 2.3 |0.48928 |0.48956 |0.48983 |0.49010 |0.49036 |0.49061 |0.49086 |0.49111 | 0.49134 |0.49158 | | 2.4 |0.49180 |0.49202 |0.49224 |0.49245 |0.49266 | 0.49286 |0.49305 |0.49324 |0.49343 |0.49361 | | 2.5 |0.49379 |0.49396 |0.49413 |0.49430 |0.49446 |0.49461 |0.49477 |0.49492 |0.49506 |0.49520 | | 2.6 |0.49534 |0.49547 |0.49560 |0.49573 |0.49585 |0.49598|0.49609 |0.49621 |0.49632 |0.49643 | | 2.7 |0.49653 |0.49664 |0.49674 |0.49683 |0.49693 |0.49702 |0.49711 |0.49720 |0.49728 |0.49736 | | 2.8 |0.49744 |0.49752 |0.49760 |0.49767 |0.49774 |0.49781 |0.49788 |0.49795 |0.49801 |0.49807 | | 2.9 |0.49813 |0.49819 |0.49825 |0.49831 |0.49836 |0.49841 |0.49846 |0.49851 |0.49856 |0.49861 | | 3.0 |0.49865 |0.49869 |0.49874 |0.49878 |0.49882 |0.49886...
Instrucciones: Resuelve el siguiente caso.
El tiempo de vida útil de un modelo de focos tiene una distribución de probabilidad normal con una media de 750 horas y una desviación típica de 40 horas.
a) Encuentra la probabilidad de que un foco dure 800 horas.
Utilizando la distribución normal tipificada, encuentra la probabilidad de que unabombilla dure menos de 784 horas.
Se sabe que la duración, en horas, de un foco de 75 watts tiene una distribución aproximadamente normal, con una desviación estándar de = 25 horas. Se toma una muestra aleatoria de 20 focos, la cual resulta tener una duración promedio de x = 1014 horas.
Construya un intervalo de confianza bilateral del 95% para la duración promedio.
|Distribución normalestándar |
Z | .00 | .01 |.02 |.03 |.04 | .05 |.06 |.07 |.08 |.09 | | 0.0 |0.00000 |0.00399 |0.00798 |0.01197 |0.01595 |0.01994 |0.02392 |0.02790 |0.03188 |0.03586 | | 0.1 |0.03983 |0.04380 |0.04776 |0.05172 |0.05567 |0.05962 |0.06356 |0.06749 |0.07142 |0.07535 | | 0.2 |0.07926|0.08317 |0.08706 |0.09095 |0.09483 |0.09871 |0.10257 |0.10642 |0.11026 |0.11409 | | 0.3 |0.11791 |0.12172 |0.12552 |0.12930 |0.13307 |0.13683 |0.14058 |0.14431 |0.14803 |0.15173 | | 0.4 |0.15542 |0.15910 |0.16276 |0.16640 |0.17003 |0.17364 |0.17724 |0.18082 |0.18439 |0.18793 | | 0.5 |0.19146 |0.19497 |0.19847 |0.20194 |0.20540 |0.20884 |0.21226 |0.21566 |0.21904 |0.22240 | | 0.6 |0.22575 |0.22907|0.23237 |0.23565 |0.23891 |0.24215 |0.24537 |0.24857 |0.25175 |0.25490 | | 0.7 |0.25804 |0.26115 |0.26424 |0.26730 |0.27035 |0.27337 |0.27637 |0.27935 | 0.28230 |0.28524 | | 0.8 |0.28814 |0.29103 |0.29389 |0.29673 |0.29955 |0.30234 |0.30511 |0.30785 |0.31057 |0.31327 | | 0.9 |0.31594 |0.31859 |0.32121 |0.32381 |0.32639 |0.32894 |0.33147 |0.33398 |0.33646 |0.33891 | | 1.0 |0.34134 |0.34375 |0.34614|0.34849 |0.35083 |0.35314 |0.35543 |0.35769 |0.35993 |0.36214 | | 1.1 |0.36433 |0.36650 |0.36864 |0.37076 | 0.37286 |0.37493 |0.37698 |0.37900 |0.38100 |0.38298 | | 1.2 |0.38493 |0.38686 |0.38877 |0.39065 |0.39251 | 0.39435 |0.39617 |0.39796 |0.39973 |0.40147 | | 1.3 |0.40320 |0.40490 |0.40658 |0.40824 |0.40988 |0.41149 |0.41308 |0.41466 |0.41621 |0.41774 | | 1.4 |0.41924 |0.42073 |0.42220|0.42364 |0.42507 |0.42647 |0.42785 |0.42922 |0.43056 |0.43189 | | 1.5 |0.43319 |0.43448 |0.43574 |0.43699 |0.43822 |0.43943 |0.44062 |0.44179 |0.44295 |0.44408 | | 1.6 |0.44520 |0.44630 |0.44738 |0.44845 |0.44950 |0.45053 |0.45154 |0.45254 |0.45352 |0.45449 | | 1.7 |0.45543 |0.45637 |0.45728 |0.45818 |0.45907 |0.45994 |0.46080 |0.46164 |0.46246 |0.46327 | | 1.8 |0.46407 |0.46485 |0.46562 |0.46638|0.46712 |0.46784 |0.46856 |0.46926 |0.46995 |0.47062 | | 1.9 |0.47128 |0.47193 |0.47257 |0.47320 |0.47381 |0.47441 |0.47500 |0.47558 |0.47615 |0.47670 | | 2.0 |0.47725 |0.47778 |0.47831 |0.47882 |0.47932 |0.47982 |0.48030 |0.48077 |0.48124 |0.48169 | | 2.1 |0.48214 |0.48257 |0.48300 |0.48341 |0.48382 |0.48422 |0.48461 |0.48500 |0.48537 |0.48574 | | 2.2 |0.48610 |0.48645 |0.48679 |0.48713 |0.48745|0.48778 |0.48809 |0.48840 |0.48870 |0.48899 | | 2.3 |0.48928 |0.48956 |0.48983 |0.49010 |0.49036 |0.49061 |0.49086 |0.49111 | 0.49134 |0.49158 | | 2.4 |0.49180 |0.49202 |0.49224 |0.49245 |0.49266 | 0.49286 |0.49305 |0.49324 |0.49343 |0.49361 | | 2.5 |0.49379 |0.49396 |0.49413 |0.49430 |0.49446 |0.49461 |0.49477 |0.49492 |0.49506 |0.49520 | | 2.6 |0.49534 |0.49547 |0.49560 |0.49573 |0.49585 |0.49598|0.49609 |0.49621 |0.49632 |0.49643 | | 2.7 |0.49653 |0.49664 |0.49674 |0.49683 |0.49693 |0.49702 |0.49711 |0.49720 |0.49728 |0.49736 | | 2.8 |0.49744 |0.49752 |0.49760 |0.49767 |0.49774 |0.49781 |0.49788 |0.49795 |0.49801 |0.49807 | | 2.9 |0.49813 |0.49819 |0.49825 |0.49831 |0.49836 |0.49841 |0.49846 |0.49851 |0.49856 |0.49861 | | 3.0 |0.49865 |0.49869 |0.49874 |0.49878 |0.49882 |0.49886...
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