Step 1
The confidence interval for the population mean, when the population standard deviations, is known the z-confidence interval as follows:
In this case, are the sample mean, population standard deviation, population mean and sample size of the population, respectively and is the critical value of the standard normal distribution, above which, proportion of the observations lie.
Step 2
The sample mean is, , the population standard deviation is and the sample size is . If 95% of the observations must lie within an interval, the remaining 5% must lie outside the interval. Further, due to symmetry, 2.5% will lie above the upper limit and the remaining 2.5% will lie below the lower limit of the interval. Thus, the upper limit of the interval is such that, 97.5% lie below it. As a result, [Using Excel formula: =NORM.S.INV(0.975)]. Thus, the confidence interval is,
(2.502, 2.698) Thus, the 95% confidence interval for the mean zinc concentration in the river is (2.502 grams per liter, 2.698 grams per liter).