A 95% confidence interval uses a procedure with 95% long-run coverage under its assumptions. The parameter is fixed; this does not assign it a 95% probability after an interval is calculated. For a two-sided z interval, the central 95% of the standard normal distribution lies between −z* and +z*.

The critical z-value for a two-sided 95% confidence interval is approximately 1.959964, usually rounded to 1.96.

How to calculate the Z-score for 95% confidence interval

A Z-table provides the area (probability) to the left of a Z-score in a standard normal distribution. Here’s how to use it for a 95% confidence interval:

  1. Determine tail areas: The area outside the central 95% is 5%. Split it equally: 2.5% in each tail of the standard normal distribution.
  2. Calculate cumulative area: At the positive critical value, the area to the left is (95% + 2.5%)/100 = 0.975. Equivalently, use (1 + 0.95)/2.
  3. Find the critical value: Look for cumulative area 0.975 in a standard normal table, or calculate its inverse CDF. This gives z* ≈ 1.959964. Use −z* and +z* as the two critical bounds.

Below is a Z-table and how it was used to identify the Z-score for a 95% confidence interval.

Calculate Z-score for 95% confidence interval
Table 1: Look up the 0.975 value in the table. It’s the intersection of 1.9 and 0.06, meaning that your Z-score is approximately 1.96.