A 97% confidence interval uses a procedure with 97% long-run coverage under its assumptions. The parameter is fixed; this does not assign it a 97% probability after an interval is calculated. For a two-sided z interval, the central 97% of the standard normal distribution lies between −z* and +z*.

The critical z-value for a two-sided 97% confidence interval is approximately 2.170090, usually rounded to 2.17.

How to calculate the Z-score for 97% 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 97% confidence interval:

  1. Determine tail areas: The area outside the central 97% is 3%. Split it equally: 1.5% in each tail of the standard normal distribution.
  2. Calculate cumulative area: At the positive critical value, the area to the left is (97% + 1.5%)/100 = 0.985. Equivalently, use (1 + 0.97)/2.
  3. Find the critical value: Look for cumulative area 0.985 in a standard normal table, or calculate its inverse CDF. This gives z* ≈ 2.170090. 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 97% confidence interval.

Calculate Z-score for 97% confidence interval
Table 1: Look up the 0.985 value in the table. It’s the intersection of 2.1 and 0.07, meaning that your Z-score is approximately 2.17.