Question

suppose the heights of the members of a population follow a normal distribution. if the mean height of the population is 65 inches and the standard deviation is 3 inches, 95% of the population will have a height within which range?

choice

a. 59 inches to 71 inches
b. 53 inches to 77 inches
c. 56 inches to 74 inches
d. 62 inches to 68 inches

Explanation:

Step1: Recuerda la regla empírica

Para una distribución normal, el 95% de los datos está dentro de \( \mu \pm 2\sigma \), donde \( \mu \) es la media y \( \sigma \) la desviación estándar.

Step2: Calcula los límites

Dado \( \mu = 65 \) y \( \sigma = 3 \), los límites son \( 65 - 2\times3 \) y \( 65 + 2\times3 \).
Calcula: \( 65 - 6 = 59 \) y \( 65 + 6 = 71 \).

Answer:

A. 59 inches to 71 inches