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[size=150]El cierre de bancos por problemas financieros ha ocurrido a razón de 5,7 clausuras por año,[/size][br][br][color=#ff7700]a) encuentre la probabilidad de que ningún banco sea cerrado durante un período de cuatro meses,[/color][br][list][*] tenemos promedio de ocurrencia al año que es [math]\lambda=5,7[/math] , debemos calcular el promedio para el periodo de cuatro meses que nos plantea el problema, por ende:[/*][/list][br] [math]\lambda_{_{_4}}=\frac{5,7}{3}=1,9[/math][br][color=#ff7700]DATOS:[br][br][math]\lambda=1,9[/math][/color][br][math]n=0[/math][br] [math]P\left(x\right)=\frac{\lambda^xe^{^{-\lambda}}}{x!}[/math][br] [math]P\left(x\right)=\frac{1,9^0.e^{-1,9}}{0!}[/math] [math]P\left(X\right)=\frac{1.e^{-1,9}}{1}[/math][br] [math]P\left(x\right)=0,1496=14,96\%[/math]

[color=#ff7700]b) por lo menos un banco sea cerrado durante el semestre[/color][br][list][*] vamos a calcular el promedio de ocurrencia, pero en este caso hablamos de semestre, es decir seis meses, entonces tenemos que: [/*][/list] [math]\frac{12}{6}=2[/math] [math]\lambda=\frac{5,7}{2}=2,85[/math] [math]x\ge1[/math] número de casos favorables[br] [math]P\left(x\ge1\right)=1\left[P\left(X=0\right)\right][/math][br] [math]P\left(X\ge1\right)=1-\left(\frac{2,85^0.e^{-2,85}}{0!}\right)[/math][br] [math]p\left(x\ge1\right)=1-0,0578[/math][br] [math]P\left(x\ge1\right)=0,9421=94,21\%[/math][br]