suppose that the heights of adult men in the United states are approximately normally distributed with a mean of 70 inches and a standard deviation of 4 inches
A) what percent of adult men in the United States should you expect to be shorter than 70 inches

Given that the heights of adult men in the United States are normally distributed with a mean (μ) of 70 inches and a standard deviation (σ) of 4 inches, we are asked to determine the percentage of adult men shorter than 70 inches.

### Solution:

A) **Percentage of Adult Men Shorter than 70 Inches:**

In a normal distribution, the mean (μ) is the center point, and the data is symmetrically distributed around it. For a normal distribution:

- The mean height (μ) is 70 inches.
- The standard deviation (σ) is 4 inches.

Since we are asked to find the percentage of men shorter than 70 inches, we need to compute the proportion of the population that falls below the mean.

In a normal distribution:
- 50% of the population lies below the mean (μ).

Thus, **50% of adult men in the United States are expected to be shorter than 70 inches.**

### Conclusion:
The percentage of adult men shorter than 70 inches is **50%**.

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Do you have any questions or need further clarification?

Here are 5 related questions:
1. What percentage of adult men are taller than 70 inches?
2. How would you calculate the percentage of men shorter than 68 inches?
3. What percentage of men fall between 66 and 74 inches in height?
4. How would the distribution change if the standard deviation were 3 inches instead of 4?
5. What is the z-score for a height of 72 inches?

**Tip:** In a normal distribution, the z-score helps you measure how many standard deviations an element is from the mean.

Explore how to calculate the percentage of adult men shorter than 70 inches in a normal distribution with a mean of 70 inches and a standard deviation of 4 inches. Understand the concept of normal distribution and its application in statistical analysis.

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