Final answer:
The z-score for an 81% confidence interval is approximately 1.41, found by looking up the area of 0.9525 in the z-table or using statistical software, since 4.75% of the area is in each tail.
Step-by-step explanation:
The z-score associated with an 81% confidence interval is not typically included in the commonly referred to empirical rule, which mentions the 68-95-99.7 rule. To find the specific z-score for an 81% confidence interval, we refer to z-tables or use statistical software.
According to the empirical rule, we know that approximately 95% of values lie within z-scores of −2 and +2, and about 99.7% lie within z-scores of −3 and +3. However, for an 81% confidence interval, we need a z-score that leaves 9.5% in the tails (4.75% in each tail). By looking up the area to the left in the z-table or using a calculator, we find the z-score that corresponds to the area of 0.9525 (1 - 0.0475), which is approximately 1.41.
In statistics, a 81% confidence interval corresponds to a z-score of approximately 1.285. This means that the critical value, or the number of standard deviations away from the mean, is 1.285.
The confidence interval represents the range within which we can be 81% confident that the true population parameter lies.