Question

Question 23 of 25 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?

Answer 1

D. 59 inches to 71 inches

Explanation:

The following is the empirical rule we use to find the range:

• the values within one standard deviation of the mean account for about 68% of the set
• within two standard deviations account for about 95%;
• within three standard deviations account for about 99.7%.

Since we are concerned about the second case the range of values will be
X = μ ± 2σ which will account for 95% of the values
where μ = mean, σ = standard deviation

So the range is

μ - 2σ ≤ X ≤ μ + 2σ

Given μ =65 inches, σ = 3inches:
65 - 2(3) ≤ X ≤ 65 + 2(3)
65 - 6 ≤ X ≤ 65+6

59 ≤ X ≤ 71
which is choice D. 59 inches to 71 inches