Question
The time it takes to edit a successful resume is normally distributed with a population standard deviation of 8 minutes and an unknown population mean. A random sample of 25 resume editors is taken and results in a sample mean of 58 minutes.

Identify the parameters needed to calculate a confidence interval at the $99 \%$ confidence level. Then use Excel to find the confidence interval.

Round the final answer to two decimal places.

Provide your answer below:
\[
\bar{x}=
\]
\[
\sigma=
\]
\[
n=
\]

Step 1 ：The problem provides the following information: the sample mean (\(\bar{x}\)) is 58 minutes, the population standard deviation (\(\sigma\)) is 8 minutes, and the sample size (\(n\)) is 25.

Step 2 ：We are asked to calculate a confidence interval at the 99% confidence level. The parameters needed for this calculation are the sample mean (\(\bar{x}\)), the population standard deviation (\(\sigma\)), and the sample size (\(n\)).

Step 3 ：Using these values, we can calculate the confidence interval. The formula for a confidence interval is \(\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}\), where \(Z\) is the Z-score corresponding to the desired confidence level.

Step 4 ：For a 99% confidence level, the Z-score is approximately 2.576.

Step 5 ：Substituting the given values into the formula, we get \(58 \pm 2.576 \frac{8}{\sqrt{25}}\).

Step 6 ：Solving this expression gives us the confidence interval (53.88, 62.12).