Given sample informatio: displaystyleoverline{{{x}}}={34},sigma={4},{n}={10} to calculate the following confidence intervals for displaystylemu assuming the sample is from a normal population. 99 percent confidence. (Round your answers to 4 decimal places.)

Given sample informatio: $\stackrel{―}{x}=34,\sigma =4,n=10$ to calculate the following confidence intervals for $\mu$ assuming the sample is from a normal population.
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Step 1
Solution:
Given that,
Sample size $n=10$
Sample mean $\stackrel{―}{x}=34$
Population standard deviation $\sigma =4$
Step 2
99 percent confidence interval:
Critical value:
The z-critical value at $99\mathrm{%}$ confidence level is 2.58.
Margin of error:
The margin of error is calculated as given below:
$E={z}_{c}\left(\frac{\sigma }{\sqrt{n}}\right)$
$=2.58\left(\frac{4}{\sqrt{10}}\right)$
$=3.2635$
Calculation:
The $99\mathrm{%}$ confidence interval for population mean can be calculated as follows:
$CI=\stackrel{―}{x}±E$
$=34±3.2635$
$=\left(30.7365,36.2635\right)$
Hence, the $99\mathrm{%}$ confidence interval for population mean is $\left(30.7365,36.2635\right).$