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# 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. # 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.

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Confidence intervals asked 2020-10-18
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.

## Answers (1) 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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Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places $$\displaystyle<{p}<$$ Express the same answer using a point estimate and a margin of error. Give your answers as decimals, to three places.
$$\displaystyle{p}=\pm\pm$$
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