Question

the heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. men the same age have mean height 69.3 inches with standard deviation 2.8 inches. (a) what is the z-score for a woman 56 inches tall?

Answer 1

To find the z-score for a woman who is 56 inches tall, we can use the formula:

Z = (X - μ) / σ

Where:
X = 56 inches (observed value)
μ = 64 inches (mean)
σ = 2.7 inches (standard deviation)

Substituting the given values into the formula, we get:

Z = (56 - 64) / 2.7
Z = -8 / 2.7
Z ≈ -2.963

Therefore, the z-score for a woman who is 56 inches tall is approximately -2.963.