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.