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To find the sample mean \( \bar{x} \) from the given confidence interval, we can use the formula:

\[
\bar{x} = \frac{\text{Lower bound} + \text{Upper bound}}{2}
\]

Here, the confidence interval is given as (61.1, 67.3). Therefore, the sample mean is:

\[
\bar{x} = \frac{61.1 + 67.3}{2} = \frac{128.4}{2} = 64.2
\]

So, the sample mean \( \bar{x} \) is 64.2.

Would you like more details, or do you have any questions? Here are some related questions to consider:

1. How does the confidence interval affect the interpretation of the sample mean?
2. What is the significance of a 95% confidence interval in this context?
3. How do you calculate the margin of error from a confidence interval?
4. What does it mean for the distribution to be "normally distributed"?
5. How can you calculate the standard deviation if the confidence interval and sample size are known?

**Tip:** Always remember that the sample mean is the midpoint of the confidence interval, which gives a good estimate of the population mean when working with normally distributed data.

The heights of American women are normally distributed. If a random sample of American women is taken and the confidence interval is (61.1, 67.3), what is the sample mean?

Learn how to calculate the sample mean from the given confidence interval (61.1, 67.3) for the heights of American women. This problem involves key statistical concepts such as confidence intervals and properties of the normal distribution, suitable for students in Grades 10-12.

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