Question

The heights of women aged 20 to 30 are approximately normal with mean 65 inches and standard deviation 2.5 inches. What is the z-score for a woman 6 feet tall?

Answer 1

To find the z-score for a woman who is 6 feet tall, we first need to convert 6 feet into inches:

1. **Convert feet to inches**:
\[
6 \text{ feet} = 6 \times 12 = 72 \text{ inches}
\]

2. **Use the z-score formula**:
The z-score is calculated using the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the value we are comparing (72 inches),
- \( \mu \) is the mean (65 inches),
- \( \sigma \) is the standard deviation (2.5 inches).

3. **Plug in the values**:
\[
z = \frac{72 - 65}{2.5}
\]
\[
z = \frac{7}{2.5}
\]
\[
z = 2.8
\]

So, the z-score for a woman who is 6 feet tall is **2.8**.