Step 1

Solution:

Given that,

Sample size \(\displaystyle{n}={10}\)

Sample mean \(\displaystyle\overline{{{x}}}={34}\)

Population standard deviation \(\displaystyle\sigma={4}\)

Step 2

99 percent confidence interval:

Critical value:

The z-critical value at \(99\%\) confidence level is 2.58.

Margin of error:

The margin of error is calculated as given below:

\(\displaystyle{E}={z}_{{c}}{\left(\frac{\sigma}{\sqrt{{n}}}\right)}\)

\(\displaystyle={2.58}{\left(\frac{4}{\sqrt{{10}}}\right)}\)

\(\displaystyle={3.2635}\)

Calculation:

The \(99\%\) confidence interval for population mean can be calculated as follows:

\(\displaystyle{C}{I}=\overline{{x}}\pm{E}\)

\(\displaystyle={34}\pm{3.2635}\)

\(\displaystyle={\left({30.7365},{36.2635}\right)}\)

Hence, the \(99\%\) confidence interval for population mean is \(\displaystyle{\left({30.7365},{36.2635}\right)}.\)