The CONFIDENCE.NORM function returns the confidence interval for a population mean, using a normal distribution. Your sample mean, x, is at the center of this range and
the range is x ± CONFIDENCE.NORM.
For example, if x is the sample mean of the length of major league baseball games, x ± CONFIDENCE.NORM is a range of population means. For any population mean, μ0, in this
range, the probability of obtaining a sample mean further from μ0 than x is greater than alpha; for any population mean, μ0, not in this range, the
probability of obtaining a sample mean further from μ0 than x is less than alpha. In other words, assume that we use x, standard_dev, and
size to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is μ0. Then we will not reject
that hypothesis if μ0 is in the confidence interval and will reject that hypothesis if μ0 is not in the confidence interval. The confidence interval does not allow us to infer that there is
probability 1 – alpha that the next game will longer than time that is in the confidence interval.