What is a standard normal distribution?

The standard normal distribution, also known as the z-distribution, is a special case of the normal distribution where the variance is always the same:

  • The mean +/- one standard deviation contains ~68% of the total variation
  • The mean +/- two standard deviations contains ~95.5% of the total variation
  • The mean +/- three standard deviations contains ~99.7% of the total variation

So, if you wanted to make a 99.7% confidence interval and your data follows a standard normal distribution, you would use a Z* of 3.