Final answer:
The z-values for 90%, 95%, and 99% confidence intervals are approximately 1.645, 1.96, and 2.58 respectively, with each value representing a point on the standard normal distribution that is further from the mean as the confidence level increases.
Step-by-step explanation:
The z-values for 90, 95, and 99 percent confidence intervals are specific points on the standard normal distribution that correspond to the tails of the distribution being excluded from these intervals.
For a 90 percent confidence interval, the critical z-value is 1.645, which means the interval captures the central 90 percent of the normal distribution and excludes 5 percent from each tail.
To obtain a 95 percent confidence interval, you would use a z-value of approximately 1.96 since it excludes 2.5 percent from each end of the distribution, making the interval wider to ensure greater certainty.
Finally, for a 99 percent confidence interval, the z-value is approximately 2.58, reflecting an interval that is wider still as it encompasses 99 percent of the distribution and only excludes 0.5 percent from each tail.