What is the z value associated with a 99% confidence interval estimation?

When constructing a confidence interval, the z value (or z-score) corresponds to the number of standard deviations a data point is from the mean and is critical for determining the margin of error in a confidence interval estimation. For a 99% confidence interval, we are interested in the area under the standard normal distribution that captures 99% of the data. This leaves 1% of the data outside the interval, split equally between the two tails of the distribution. Therefore, we have 0.5% in each tail.

To find the corresponding z value, we look for the point where 0.5% (or 0.005 in probability terms) is in the upper tail of the standard normal distribution. The z value that corresponds to the cumulative probability of 0.995 (since 1 - 0.005 = 0.995) is approximately 2.58. This means that for a 99% confidence level, we use this z value for margin calculations, allowing us to estimate the range within which we can expect our sample mean to fall with 99% certainty.

Thus, the appropriate z value for a 99% confidence interval estimation is 2.58.