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The example in the image describes the heights of young German men aged 18 to 19. Their heights follow a normal distribution with:

- Mean (average) height = 181 cm
- Standard deviation = 8 cm

Since the distribution is approximately normal, we can use the properties of a normal distribution to describe the population.

### Key characteristics of this population:
1. **68% of the population** will have heights within 1 standard deviation of the mean (181 cm ± 8 cm), i.e., between 173 cm and 189 cm.
2. **95% of the population** will have heights within 2 standard deviations, i.e., between 165 cm and 197 cm.
3. **99.7% of the population** will have heights within 3 standard deviations, i.e., between 157 cm and 205 cm.

This normal distribution suggests that most young German men in this age group will have heights clustered around 181 cm, with fewer individuals having heights that deviate significantly from this mean.

Would you like to explore more about this, or do you have any further questions?

### Related questions:
1. What is the probability of a young German man being taller than 190 cm in this population?
2. How would you calculate the height that corresponds to the 90th percentile in this group?
3. Can you explain how to find the Z-score for a height of 170 cm?
4. What would be the range of heights for the middle 50% of the population?
5. How does the standard deviation affect the spread of the heights in this population?

### Tip:
In a normal distribution, the larger the standard deviation, the more spread out the data will be around the mean.

Heights of young German men between 18 and 19 years of age follow a distribution that is approximately normal, with mean 181 cm and a standard deviation of approximately 8 cm. Describe this population of young men.

Explore the normal distribution of heights among young German men aged 18-19. With a mean of 181 cm and a standard deviation of 8 cm, learn how the Empirical Rule describes the distribution of this population. This detailed analysis is ideal for high school students in grades 10-12.

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