Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A store manager reports a confidence interval of left parenthesis 48.8 comma 81.0 right parenthesis when estimating the mean price​ (in dollars) for the population of textbooks. 
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Part 1
The estimated margin of error is 
  
enter your response here.
​(Type an integer or a​ decimal.)

To calculate the estimated margin of error from the confidence interval \((48.8, 81.0)\), we can use the following formula:

\[
\text{Margin of Error} = \frac{\text{Upper Bound} - \text{Lower Bound}}{2}
\]

In this case:

\[
\text{Margin of Error} = \frac{81.0 - 48.8}{2} = \frac{32.2}{2} = 16.1
\]

So, the estimated margin of error is **16.1**.

---

For the sample mean, we can calculate it by finding the midpoint of the confidence interval:

\[
\text{Sample Mean} = \frac{\text{Upper Bound} + \text{Lower Bound}}{2}
\]

\[
\text{Sample Mean} = \frac{81.0 + 48.8}{2} = \frac{129.8}{2} = 64.9
\]

Thus, the sample mean is **64.9**.

---

Would you like further explanation or have any questions about this process?

Here are some related questions to delve deeper:
1. How does changing the confidence level affect the margin of error?
2. What assumptions are necessary for using a confidence interval in this context?
3. How would we interpret this confidence interval in terms of textbook prices?
4. How can we use this confidence interval to make business decisions in the store?
5. What role does sample size play in determining the width of a confidence interval?

**Tip:** The margin of error increases as the confidence level increases, reflecting more certainty in capturing the population mean within the interval.

A store manager reports a confidence interval of (48.8, 81.0) when estimating the mean price (in dollars) for the population of textbooks. The estimated margin of error is (enter your response here). (Type an integer or a decimal.)

Learn how to calculate the margin of error and sample mean from a given confidence interval (48.8, 81.0) for textbook prices. This solution covers key statistical concepts like confidence intervals, margin of error, and sample means, suitable for students in Grades 9-12.

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