Question

2 multiple choice 6.67 points the heights of all 10 - year old children are normally distributed, with a mean of 138 cm and a standard deviation of 5 cm. what is the probability that a student will be greater than 133 cm (las alturas de todos los niños de 10 años se distribuyen normalmente, con una media de 138 cm y una desviación estándar de 5 cm. ¿cuál es la probabilidad de que un estudiante mida más de 133 cm?) 99.7% 84% 68% 95%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 133$, $\mu=138$, and $\sigma = 5$.
$z=\frac{133 - 138}{5}=\frac{- 5}{5}=-1$

Step2: Find the probability using the standard normal distribution

We want $P(X>133)$, which is equivalent to $P(Z>-1)$ in the standard - normal distribution. Since the total area under the standard - normal curve is 1, and $P(Z < - 1)+P(Z>-1)=1$. Looking up the value of $P(Z < - 1)$ in the standard - normal table, we find that $P(Z < - 1)=0.16$. So $P(Z>-1)=1 - 0.16 = 0.84$ or 84%.

Answer:

B. 84%