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.)

What is the z‑score for a man 5.5 feet tall? (Enter your answer rounded to two decimal places.)

Answer 1

Answer:

a) 0.64

b) -1.13      

Step-by-step explanation:

We are given the following information in the question:

Women:

Mean, μ = 64.2 inches

Standard Deviation, σ = 2.8 inches

We are given that the distribution of heights of women is a bell shaped distribution that is a normal distribution.

Men:

Mean, μ = 69.4 inches

Standard Deviation, σ = 3.0 inches

We are given that the distribution of heights of men is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

5.5 feet = 66 inches

a)  z‑score for a woman 5.5 feet tall

$x = 66\\\\\Rightqrrow z = \displaystyle\frac{66 - 64.2}{2.8} = 0.64$

b) z‑score for a man 5.5 feet tall

$x = 66\\\\\Rightqrrow z = \displaystyle\frac{66 - 69.4}{3.0} = -1.13$