Question

According to the United States Department of Health and Human Services, the mean height for Americans is 1.757 m for men and 1.618 m for women3. The standard deviation is 0.074 m for men and 0.069 m for women.

What z-score corresponds to a man who is 1.853 m tall?

Answer 1

The z-score for a man who is 1.853 meters tall is approximately 1.2973, indicating that this height is about 1.2973 standard deviations above the average height for American men.

Step-by-step explanation:

To find the z-score for a man who is 1.853 meters tall, we can use the z-score formula:

z = (X - μ) / σ

where:

• X is the value to be standardized (the man's height),
• μ (mu) is the mean of the population, and
• σ (sigma) is the standard deviation of the population.

Based on the information given:

• The mean height (μ) for American men is 1.757 meters,
• The standard deviation (σ) is 0.074 meters,
• The man's height (X) is 1.853 meters.

Thus, the z-score is calculated as follows:

z = (1.853 - 1.757) / 0.074

z = (0.096) / 0.074

z = 1.2973

This means that a man who is 1.853 meters tall is approximately 1.2973 standard deviations above the mean height for American men.