Question

In a survey of men in a certain country (ages 20 - 29), the mean height was 64.7 inches with a standard deviation of 2.9 inches. (a) What height represents the 90th percentile? (b) What height represents the first quartile?

Answer 1

Explanation:

(a) To find the height that represents the 90th percentile, we would need to use a standard normal distribution table and a Z-score. We need to first find the Z-score corresponding to the 90th percentile by solving for Z using the formula:

Z = (x - μ) / σ

Where x is the height at the 90th percentile, μ is the mean height (64.7 inches), and σ is the standard deviation (2.9 inches).

Z = (x - 64.7) / 2.9

Since the 90th percentile corresponds to a Z-score of 1.28, we can use the above formula to find x:

x = μ + Zσ

x = 64.7 + (1.28)(2.9)

x = 68.9 inches

So, the height that represents the 90th percentile is 68.9 inches.

(b) To find the first quartile (25th percentile), we would use a Z-score of -0.67.

x = μ + Zσ

x = 64.7 + (-0.67)(2.9)

x = 62.3 inches

So, the height that represents the first quartile is 62.3 inches.