# How to solve this confidence interval? Use the confidence interval to find the estimated margin of error. Then find the sample mean. A store manager says a confidence interval of (44.07, 80.97) when estimating the mean price (in dollars) for the population of textbooks.

Question
Confidence intervals
How to solve this confidence interval? Use the confidence interval to find the estimated margin of error. Then find the sample mean. A store manager says a confidence interval of (44.07, 80.97) when estimating the mean price (in dollars) for the population of textbooks.

2020-10-19
Given a confidence interval (44.07, 80.97)
As confidence interval is $$\overline{x}=\pm E,(\overline{x}+E)-(\overline{x}-E)=2E$$ where $$\overline{x}$$ is mean price of sample of textbooks and E is margin of error.
Thus, $$E=\frac{80.97-44.07}{2}=18.45$$
Now, $$\overline{x} - E = 44.07$$
Hence, $$\overline{x} = 44.07 + 18.45 = 65.52$$ is mean price of sample textbooks
Answer: $$E = 18.45$$
$$\overline{x} = 62.52$$

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