Question

question 9 of 25
suppose the heights of the members of a population follow a normal distribution. if the mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height within which range?
a. 63 inches to 81 inches
b. 60 inches to 84 inches
c. 69 inches to 75 inches
d. 66 inches to 78 inches

Explanation:

Step1: Recall 68-95-99.7 rule

For normal distribution, 99.7% data is within $\mu \pm 3\sigma$.

Step2: Calculate lower bound

$\mu - 3\sigma = 72 - 3\times3 = 63$ inches.

Step3: Calculate upper bound

$\mu + 3\sigma = 72 + 3\times3 = 81$ inches.

Answer:

A. 63 inches to 81 inches