Question

The heights of women aged 20 – 29 in the United States are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. The heights of men aged 20 – 29 in the United States are approximately Normal with mean 69.4 inches and standard deviation 3.0 inches. What is the z ‑score for a woman 5.5 feet tall? (Enter your answer rounded to two decimal places.)

Answer 1

Answer: 0.64

Step-by-step explanation:

Given : The heights of women aged 20 – 29 in the United States are approximately Normal with $\mu=64.2$ inches and $\sigma=2.8$ inches.

Let x denotes the height of women.

Since 1 feet = 12 inches

5.5 feet = $5.5\times12=66$ inches

Then, the z-score corresponds to x=66 inches will be :-

$z=\dfrac{66-64.2}{2.8}=0.642857142857\approx0.64$

Hence, the z ‑score for a woman 5.5 feet tall = 0.64