select the correct answer.\nthe numbers of pages in the books in a library follow a normal distribution. if…

select the correct answer.\nthe numbers of pages in the books in a library follow a normal distribution. if the mean number of pages is 180 and the standard deviation is 30 pages, what can you conclude?\na. about 60% of the books have fewer than 150 pages.\nb. about 16% of the books have fewer than 150 pages.\nc. about 95% of the books have more than 150 pages.\nd. about 16% of the books have more than 150 pages.

select the correct answer.\nthe numbers of pages in the books in a library follow a normal distribution. if the mean number of pages is 180 and the standard deviation is 30 pages, what can you conclude?\na. about 60% of the books have fewer than 150 pages.\nb. about 16% of the books have fewer than 150 pages.\nc. about 95% of the books have more than 150 pages.\nd. about 16% of the books have more than 150 pages.

Answer

Explanation:

Step1: Calcular el z - score

El z - score se calcula con la fórmula $z=\frac{x-\mu}{\sigma}$, donde $x = 150$, $\mu=180$ y $\sigma = 30$. Entonces $z=\frac{150 - 180}{30}=\frac{- 30}{30}=-1$.

Step2: Usar la regla empírica

En una distribución normal, aproximadamente el 68% de los datos está dentro de 1 desviación estándar del promedio ($z=-1$ y $z = 1$), lo que significa que el 32% de los datos está fuera de este rango. La mitad de este 32% (es decir, 16%) está por debajo de $z=-1$.

Answer:

B. About 16% of the books have fewer than 150 pages.