Guía de ejercicios - Distribución Normal
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Guía de ejercicios – Distribución Normal
1)
La media de los pesos de los estudiantes de un colegio es de 70 kg y la desviación
estándar de 3 kg. Suponga que los pesos se distribuyen normalmente, hallar la
probabilidad de que los estudiantes pesen:
a)
Menos de 64 kg.
b)
Más de 80 kg.
c)
Entre 60 y 75 kg.
2)
Tras una prueba de cultura general se observa que las puntuaciones obtenidas
siguen una distribución normal
N
(
65,324
)
. Se desea clasificar a los examinados
en tres grupos distintos (baja cultura general, cultura general aceptable y excelente
cultura general) de modo que hay en el primero un 20% de la población, un 65% en
el segundo y un 15% en el tercero. ¿Cuáles han de ser las puntuaciones que marcan
el paso de un grupo a otro?
3)
Considere una población de recién nacidos, en los cuales interesa estudiar la
variable estatura. Suponga que la estatura de los recién nacidos es una variable
aleatoria con distribución normal con media 50 cm y desviación estándar 2 cm.
a)
¿Cuál es la probabilidad de que un niño mida menos de 45 cm al nacer?
b)
¿Cuál es la probabilidad de que un niño al nacer mida a lo menos 52 cm?
c)
¿Qué porcentaje de recién nacidos mide entre 48 y 52 cm?
d)
¿Con cuántos centímetros a lo más nacen el 80% de los niños?
4)
En una prueba que mide el coeficiente intelectual de una población, se obtiene que
la variable se distribuye normalmente con media igual a 100 y desviación típica 15.
a)
Determinar el porcentaje de población que obtendría un coeficiente entre 95
y 110.
b)
¿Qué intervalo centrado en 100 contiene al 50% de la población?
Respuestas:
1)
a)
0,0228
b)
0,0004
c)
0,9511
2)
Baja cultura general hasta los 49 puntos, cultura general aceptable entre 50 y 83
puntos, excelente cultura general a partir de los 84 puntos.
3)
a)
0,0062
b)
0,1587
c)
68,26%
d)
51,7 cm
4)
a)
0,3747
b)
Entre 90 y 110 está el 50% central de la población.
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