52. En una población de trabajadores del Estado, que gozan pensión de jubilación, el 36% tiene más de 65 años. ¿Cuál es la probabilidad, en una muestra de 18 pensionados, de que 15 o más tenga más de 65 años?[br][br][color=#ff0000]DATOS:[/color][br]n=18[br]p=36%=0,36 Éxito[br]q=64%=0,64 Fracaso[br]x ≥15[br][color=#ff0000][br]DESARROLLO DEL 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[/img][br][br][br][math]P\left(x>15\right)=\frac{18!}{15!\left(18-15\right)!}.\left(0,36\right)^{15}.\left(0,64\right)^{18-15}+\frac{18!}{16!\left(18-16\right)!}.\left(0,36\right)^{16}.\left(0,64\right)^{18-16}+\frac{18!}{17!\left(18-17\right)!}.\left(0,36\right)^{17}.\left(0,64\right)^{18-17}+\frac{18!}{18!\left(18-18\right)!}.\left(0,36\right)^{18}.\left(0,64\right)^{18-18}[/math][br][br][math]P\left(x>5\right)=\frac{18.17.16}{3.2}.\left(0,36\right)^{15}.\left(0,64\right)^3+\frac{18.17}{2}.\left(0,36\right)^{16}.\left(0,64\right)^2+18\left(0,36\right)^{17}.\left(0,64\right)+1\left(0,36\right)^{18}.1[/math][br][br][math]P\left(x>15\right)=816.\left(0,36\right)^{15}.\left(0,64\right)^3+153.\left(0,36\right)^{16}.\left(0,64\right)^2+18.\left(0,36\right)^{17}.\left(0,64\right)^{ }+1.\left(0,36\right)^{18}.1[/math][math]P\left(X>15\right)=0,0000472+0,000004987+0,0000003300+0,0000000103[/math][br][math]P\left(x>5\right)=0,000052617=0,0052\varkappa[/math][br][br][br][br][/color][br][br]