Answer :
[tex]\begin{gathered} \text{Given} \\ \overline{x}=3.18 \\ s=0.07 \\ n=42 \end{gathered}[/tex]
Recall that the formula for confidence interval is determined by
[tex]\begin{gathered} CI=\bar{x}\pm z\frac{s}{\sqrt[]{n}} \\ \text{where} \\ \bar{x}\text{ is the sample mean} \\ s\text{ is the sample standard deviation} \\ n\text{ is the number of data} \\ z\text{ is the z-score of the confidence interval} \end{gathered}[/tex]A 90% confidence interval has a z-score of 1.645. Substitute the following values and we get
[tex]\begin{gathered} CI=\bar{x}\pm z\frac{s}{\sqrt[]{n}} \\ CI=3.18\pm(1.645)\frac{0.07}{\sqrt[]{42}} \end{gathered}[/tex]Solve for the upper and lower limit
[tex]\begin{gathered} \text{Upper Limit} \\ 3.18+(1.645)\cdot\frac{0.07}{\sqrt{42}}\approx3.20 \\ \\ \text{Lower Limit} \\ 3.18-(1.645)\cdot\frac{0.07}{\sqrt[]{42}}\approx3.16 \end{gathered}[/tex]Therefore, the 90% confidence interval for the population mean time is
[tex]3.16<\mu<3.2[/tex]