# A random sample of 10 items is taken from a normal population. The sample had a mean of 82 and a...

## Question:

A random sample of 10 items is taken from a normal population. The sample had a mean of 82 and a standard deviation is 26. What is the appropriate 99% confidence interval for the population mean?

## Confidence Interval for a Mean:

Confidence interval gives a range of all possible values likely to be true population mean at a stated level of confidence. The length of the interval is determined by sample size, sample variability and level of confidence used.

## Answer and Explanation:

Given that;

{eq}n=10\\\bar x=82\\\sigma=26 {/eq}

Use equation below to construct the 99% confidence interval:

{eq}\displaystyle \left(\bar X\pm z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\right) {/eq}

The critical value that corresponds to 99% level of confidence is +/-2.58:

{eq}\displaystyle \left(82\pm 2.58\times \frac{26}{\sqrt{10}}\right)\\(82\pm 21.21)\\(60.79, 103.21) {/eq}

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#### Learn more about this topic:

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3