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]}