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vivado [14]
3 years ago
14

El peso en gramos de las cajas de cereales de cierta marca siguen una distribución Normal con media de 500g y desviación de 5g [

N(500,%)] Calcula la probabilidad de encontrar una caja que pese menos de 496 gramos. ¿Qué porcentaje de cajas pesa entre 505g y 510g?
Mathematics
1 answer:
Marianna [84]3 years ago
3 0

Answer:

a) 2.1186

b) 13.591%

Step-by-step explanation:

Resolvemos usando la fórmula de puntuación z

z = (x-μ) / σ, donde

x es la puntuación bruta =

μ es la media de la población = 500g

σ es la desviación estándar de la población = 5 g

a) Calcula la probabilidad de encontrar una caja que pese menos de 496 gramos.

Para x = 496g

z = 496 - 500/5

z = -0.8

Valor de probabilidad de Z-Table:

P (x <496) = 0.21186

La probabilidad de encontrar una caja que pese menos de 496 gramos es 0.21186

b) ¿Qué porcentaje de cajas pesan entre 505 gy 510 g?

Para x = 505 g

z = 505 - 500/5

z = 1

Valor de probabilidad de Z-Table:

P (x = 505) = 0.84134

Para x = 510g

z = 510 - 500/5

z = 2

Valor de probabilidad de Z-Table:

P (x = 510) = 0.97725

La probabilidad de cajas que pesen entre 505 gy 510 g

P (x = 510) - P (x = 505)

= 0.97725 - 0.84134

= 0.13591

Conversión a porcentaje

= 0.13591 × 100

= 13.591%

El porcentaje de cajas que pesan entre 505g y 510g es del 13.591%

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