This section explains how to compute a confidence interval for the mean of a normally-distributed variable for which the population standard deviation is known. In practice, the population standard deviation is rarely known. However, learning how to compute a confidence interval when the standard deviation is known is an excellent introduction to how to compute a confidence interval when the standard deviation has to be estimated.

Three values are used to construct a confidence interval for μ: the sample mean (M), the value of z (which depends on the level of confidence), and the standard error of the mean (σ

M - z σ

Assume that the standard deviation of SAT verbal scores in a school system is known to be 100. A researcher wishes to estimate the mean SAT score and compute a 95% confidence interval from a random sample of 10 scores.