Construct the confidence interval for the population mean $\mu$.
\[
c=0.90, \bar{x}=5.4, \sigma=0.3, \text { and } n=58
\]
A $90 \%$ confidence interval for $\mu$ is (Round to two decimal places as needed.)

Step 1 ：Given that the sample mean (\(\bar{x}\)) is 5.4, the standard deviation (\(\sigma\)) is 0.3, the sample size (\(n\)) is 58, and the confidence level (\(c\)) is 0.90.

Step 2 ：The z-score for a 90% confidence level is approximately 1.645. This value can be found in a standard z-table or calculated using a statistical function.

Step 3 ：The confidence interval for a population mean can be calculated using the formula: \(\bar{x} \pm z \frac{\sigma}{\sqrt{n}}\)

Step 4 ：Substitute the given values into the formula to calculate the confidence interval: \(5.4 \pm 1.645 \frac{0.3}{\sqrt{58}}\)

Step 5 ：Calculate the margin of error: \(1.645 \frac{0.3}{\sqrt{58}} \approx 0.065\)

Step 6 ：Calculate the lower limit of the confidence interval: \(5.4 - 0.065 \approx 5.34\)

Step 7 ：Calculate the upper limit of the confidence interval: \(5.4 + 0.065 \approx 5.46\)

Step 8 ：\(\boxed{\text{Final Answer: The 90% confidence interval for } \mu \text{ is approximately } (5.34, 5.46)}\)