Because we can compute the population standard deviation, we use the z-statistic. A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size (note that the population variance is given and its positive square root is the standard deviation of the population): x ± zα/2 × ( σ / n1/2) = 96 ± 1.96 × (91/2 / 4001/2) = 96 ± 1.96 × (0.15) = 96 ± 0.294 = 95.706 to 96.294.
