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, 99.7% of the population will have a height
within which range?
a. 59 inches to 71 inches
b. 53 inches to 77 inches
c. 62 inches to 68 inches
d. 56 inches to 74 inches

Answer 1

D) 56 inches to 74 inches

Explanation:

By the Empirical Rule, 99.7% of data in a normal distribution spread across ±3σ standard deviations from the mean μ.

Hence, the range maximum is μ+3σ = 65+3(3) = 65+9 = 74 inches, and the range minimum is μ-3σ = 65-3(3) = 65-9 = 56 inches

Thus, 99.7% of the population will have a height within the range of 56 inches to 74 inches