Presentacin de PowerPoint
La distribucinNORMAL
Conociendo la distribucin normal
La distribucin normal
Una variable aleatoria contnua es aquella que puede asumir un
nmero infinito de valores dentro de cierto rango
especfico.Recordemos
La familia de las distribuciones de probabilidad normal Cada una
de las distribuciones puede tener una media distinta (u) y
desviacin estndar distinta (). No existe una sola distribucin de
probabilidad normal, sino ms bien se trata de toda una familia de
ellas. Por tanto, eI nmero de distribuciones normales es
ilimitado.
Al variar los parmetros and , obtenemos diferentes
distribuciones normalesLa familia de las distribuciones de
probabilidad normalLa familia de las distribuciones de probabilidad
normalXf(X)Cambiando movemos la distribucin lhacia la izquierda o
derecha.Cambiando aumentamos o disminumos su altura..La curva
normal tiene forma de campana y un slo pico en el centro de la
distribucin. La distribucin de probabilidad normal y la curva
normal que la acompaa tienen las siguientes caractersticas:
El promedio aritmtico, la mediana y la moda de la distribucin
son iguales y se ubican en el pico.
Caractersticas (cont.)Caractersticas (cont.)La mitad del rea
bajo la curva se encuentra a la derecha de este punto central y la
otra mitad est a la izquierda de dicho punto.
Caractersticas (cont.)
Es simtrica en torno a su promedio. Si se corta Ia curva normal
de manera vertical por el valor central, las dos mitades sern como
imgenes en un espejo.Caractersticas (cont.)
La curva normal desciende suavemente en ambas direcciones a
partir del valor central. Es asinttica, Ia curva se acerca cada vez
ms al eje de X pero jams llega a tocarlo. Es decir, las colas de Ia
curva se extienden de manera indefinida en ambas
direcciones.Caractersticas (cont.)
La distribucin de probabilidad normal estndarSera fsicamente
imposible proporcionar una tabla de probabilidades para cada
combinacin de u y (como para Ia distribucin binomial o para Ia de
Poisson) .Es posible utilizar un slo miembro de Ia familia de
distribuciones normales para todos los problemas en los que se
aplica Ia distribucin normal.
La distribucin de probabilidad normal estndarTiene una media de
0 y una desviacin estndar de 1 Los valores mayores al promedio
tienen valores Z positivos y, valores menores al promedio tendrn
valores Z negativos.Zf(Z)10La distribucin de probabilidad normal
estndarUtilizando un valor z, se convertir, o estandarizar, Ia
distribucin real a una distribucin normal estndar. Transformamos
unidades X en unidades Z Todas las distribuciones normales pueden
convertirse a distribucin normal estndar restando Ia media de cada
observacin y dividiendo por Ia desviacin estndar.Un valor z es Ia
distancia a partir de Ia media, medida en las unidades de desviacin
estndar.El valor z
Valor z = Ia distancia entre un valor seleccionado (x) y Ia
media (u), dividida por la desviacin estndar ().
El valor z
Lmites sigma
Lmites dos sigma
Lmites tres
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