# find a confidence interval for estimating the population mean µ. The confidence level is 95% and for the sample data, sample size n=92, mean=90.6 and population standard deviation σ=8.9

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justaguide | Certified Educator

For a confidence level of 95% the sample means fall within 1.96 standard errors of the population mean.

This is used to calculate the confidence interval, where mean is 90.6, the population standard deviation is `sigma = 8.9` and the sample size is n = 92.

The confidence interval in which `mu` lies is given by `bar X -1.96*(sigma/sqrt n)` and `bar X + 1.96*(sigma/sqrt n)`

`90.6 - 1.96*(8.9/sqrt 92) = 88.78`

`90.6 + 1.96*(8.9/sqrt 92) = 92.42`

**The confidence interval is **`88.78 < mu < 92.42`

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