the life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation…

the life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

the life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

Answer

Explanation:

Step1: Escribir la fórmula de estandarización

La fórmula para estandarizar una variable $X$ que sigue una distribución normal $N(\mu,\sigma)$ es $z=\frac{x - \mu}{\sigma}$, donde $\mu$ es la media, $\sigma$ es la desviación estándar y $x$ es el valor de interés.

Step2: Sustituir valores dados

Dado que $\mu = 128$, $\sigma=16$ y $x = 100$, entonces $z=\frac{100 - 128}{16}$.

Step3: Realizar el cálculo

$z=\frac{- 28}{16}=-\frac{7}{4}=-1.75$

Answer:

$-1.75$