Final answer:
The confidence level for the interval x ± 2.81σ/√n is 99%. This is determined by the correspondence of the z-score to the confidence level in the z-score table.
Step-by-step explanation:
The confidence level associated with x ± 2.81σ/√n is 99%. This can be determined by looking at the z-score table or standard normal distribution table, wherein a z-score of approximately 2.81 corresponds to a 99% confidence level. In statistical terms, a confidence interval gives an estimated range of values that is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
If we were to take repeated samples, approximately 99 percent of those confidence intervals calculated from those samples would contain the true value of the population mean. It's essential to understand that the wider the confidence interval, the greater the confidence level. For example, a 95 percent confidence interval would be wider than that of a 90 percent confidence interval, because it has to encompass a greater area under the normal distribution to assure that it captures the population mean 95 percent of the time.