Question

In a survey of women in the United States (ages 20-29). the mean height was 64.2 inches with a standard deviation of 2.9 inches. (Adapted from National Center for Health Statistics) What height represents the 95th percentile? What height represents the first quartile? Heights of Men In a survey of men in the United States (ages 20-29). the mean height was 69.4 inches with a standard deviation of 2.9 inches (Adapted from National Center for Health Statistics) What height represents the 90th percentile? What height represents the first quartile?

Answer 1

The height that represents the 95th percentile for women is approximately 68.972 inches, and the height that represents the first quartile is approximately 62.244 inches. For men, the height that represents the 90th percentile is approximately 73.123 inches, and the height that represents the first quartile is approximately 67.444 inches.

Step-by-step explanation:

To find the height that represents the 95th percentile in the survey of women, we can use the standard normal distribution table or a calculator. The z-score corresponding to a 95th percentile is approximately 1.645. We can calculate the height as:

Height = Mean + (Z-score imes Standard Deviation)

Height = 64.2 + (1.645 imes 2.9)

Height = 64.2 + 4.772

Height ≈ 68.972 inches

The height that represents the first quartile can be calculated as:

Height = Mean - (Z-score imes Standard Deviation)

Height = 64.2 - (0.6745 imes 2.9)

Height = 64.2 - 1.95605

Height ≈ 62.244 inches

For the survey of men, to find the height that represents the 90th percentile, we use a similar calculation:

Height = Mean + (Z-score imes Standard Deviation)

Height = 69.4 + (1.282 imes 2.9)

Height = 69.4 + 3.7238

Height ≈ 73.123 inches

The height that represents the first quartile can be calculated as:

Height = Mean - (Z-score imes Standard Deviation)

Height = 69.4 - (0.6745 imes 2.9)

Height = 69.4 - 1.95605

Height ≈ 67.444 inches