Step 1
State the formula for the confidence interval
[tex]\bar{x}\pm z_{\frac{\alpha}{2}}\times(\frac{\sigma}{\sqrt[]{n}})[/tex]
Where;
[tex]\begin{gathered} \bar{x}=mean=63\text{ ounces} \\ \sigma=\text{ standard deviation = 4 ounces} \\ n=\text{ 38 backpacks} \\ z_{\frac{\alpha}{2}}=z_{0.005}=2.576 \end{gathered}[/tex]
Step 2
Find the margin of error, E
[tex]\begin{gathered} E=z_{\frac{\alpha}{2}}\times(\frac{\sigma}{\sqrt[]{n}}) \\ E=2.576\times\frac{4}{\sqrt[]{38}} \\ E=\text{ }1.671529523 \\ E\approx\text{ 1.67 to 2 decimal places} \end{gathered}[/tex]
Step 3
Find the final answer
[tex]63\pm1.67\text{ ounces to 2 decimal places}[/tex]
