when zahra commutes to work, the amount of time it takes her to arrive is normally distributed with a mean…
when zahra commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes. what is the probability that on a given day, her commute will be longer than 38 minutes, to the nearest thousandth?\nstatistics calculator
Answer
Explanation:
Step1: Calcular el z - score
El fórmula para el z - score es $z=\frac{x-\mu}{\sigma}$, donde $x = 38$ (valor de interés), $\mu = 28$ (media) y $\sigma=4.5$ (desviación estándar). $z=\frac{38 - 28}{4.5}=\frac{10}{4.5}\approx2.222$
Step2: Encontrar la probabilidad correspondiente al z - score
Buscamos $P(Z>2.222)$ en la tabla normal estandarizada. Sabemos que $P(Z < z)+P(Z>z)=1$. Buscando en la tabla, $P(Z < 2.222)\approx0.9868$. Entonces $P(Z>2.222)=1 - 0.9868 = 0.0132\approx0.013$
Answer:
$0.013$