the times of all 15 - year - olds who run a certain race are approximately normally distributed with a given…

the times of all 15 - year - olds who run a certain race are approximately normally distributed with a given mean $mu = 18$ sec and standard deviation $sigma = 1.2$ sec. what percentage of the runners have times less than 14.4 sec?\n0.15%\n0.30%\n0.60%\n2.50%

the times of all 15 - year - olds who run a certain race are approximately normally distributed with a given mean $mu = 18$ sec and standard deviation $sigma = 1.2$ sec. what percentage of the runners have times less than 14.4 sec?\n0.15%\n0.30%\n0.60%\n2.50%

Answer

Explanation:

Step1: Calcular el z - score

El fórmula del z - score es $z=\frac{x-\mu}{\sigma}$, donde $x = 14.4$, $\mu = 18$ y $\sigma=1.2$. $z=\frac{14.4 - 18}{1.2}=\frac{- 3.6}{1.2}=-3$

Step2: Buscar la probabilidad en la tabla normal

Buscamos la probabilidad correspondiente a $z = - 3$ en la tabla normal estándar. La probabilidad $P(Z < - 3)$ es de 0.0015.

Step3: Convertir la probabilidad a porcentaje

Multiplicamos la probabilidad por 100 para obtener el porcentaje. $0.0015\times100 = 0.15%$

Answer:

0.15%