What is the Z-value corresponding to a 90% confidence level?

At a 90% confidence level, the Z-value reflects the point in the standard normal distribution beyond which only 10% of the data lies. To find this value, you would look for the Z-value that corresponds to the upper tail of the distribution.

In standard normal distribution terms, a 90% confidence level means that 5% of the area is in each tail of the distribution (since the total area under the curve is 100%). This leaves 90% in the middle. The Z-value that corresponds to the cumulative probability of 0.95 (which accounts for the 90% in the middle plus the 5% in the upper tail) is approximately 1.645. For practical purposes in many scenarios, it is often rounded to 1.65.

Therefore, the Z-value for a 90% confidence level is correctly identified as 1.65, representing the point at which the probability of a value falling below it is 90%. This understanding is crucial for applications in financial risk management, particularly in value-at-risk (VaR) calculations and other risk assessments.