Question

You measure 48 randomly selected textbooks' weights, and find they have a mean weight of 69 ounces. Assume the population standard devlation is 5.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook welght. Give your answers as decimals, to two places <p<

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Answer to a math question You measure 48 randomly selected textbooks' weights, and find they have a mean weight of 69 ounces. Assume the population standard devlation is 5.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook welght. Give your answers as decimals, to two places <p<

Expert avatar
Miles
4.9
115 Answers
To construct a 95% confidence interval for the true population mean textbook weight, we can use the formula for a confidence interval:
\bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right)
Where:
- \bar{x} = 69 ounces (mean weight of the textbooks)
- \sigma = 5.3 ounces (population standard deviation)
- n = 48 textbooks
- The critical value Z = 1.96 for a 95% confidence interval

Now we can plug in the values:
69 \pm 1.96 \left( \frac{5.3}{\sqrt{48}} \right)

69 \pm 1.96 \times \frac{5.3}{\sqrt{48}}

69 \pm 1.96 \times \frac{5.3}{6.93}

69 \pm 1.96 \times 0.765

69 \pm 1.50

Therefore, the 95% confidence interval for the true population mean textbook weight is:
\textbf{[67.50, 70.50]} \, \text{ounces}

\boxed{[67.50, 70.50]}

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