In interval estimation for a proportion, what is the critical value of z at a 99% confidence level?

At a 99% confidence level, the critical value of z represents the number of standard deviations away from the mean that correlates with the desired level of confidence in the context of a standard normal distribution. To obtain the critical value for a specified confidence level, one must recognize that a 99% confidence level indicates that we want to capture the middle 99% of the distribution, leaving 1% in the tails.

This means that there is 0.5% in the lower tail and 0.5% in the upper tail of the standard normal distribution. To find the z value that corresponds to the upper tail for the 99% confidence level, you can look up the z-proportion that has an accumulated area of 0.995 (which accounts for the lower tail of 99.5% of the distribution).

Using a z-table or standard normal distribution table, one finds that the z value that provides this area is approximately 2.576. This value represents the point where the cumulative area under the standard normal curve reaches 0.995, indicating that 99% of the data falls within roughly ±2.576 standard deviations from the mean.

Thus, the critical value of z at a 99%