Final answer:
To construct a 99.1% confidence interval, you need to find the critical value zα/2 by identifying the area for each tail and then using a z-table or calculator. For a 99.1% confidence interval, the critical value is approximately zα/2 = 2.575.
Step-by-step explanation:
To find the critical value zα/2 for constructing a 99.1% confidence interval, you need to first understand that the confidence level (CL) represents the central area under the standard normal distribution. The area in the tails, α, is split equally on both sides. For a 99.1% confidence interval, α would be 1 - 0.991 = 0.009, and α/2 is 0.0045 for each tail. Using this α/2 value, you can determine the critical z-score that correlates to the desired confidence level.
As we know from the reference provided, the z-score for a 95% confidence interval (α = 0.05) is 1.96. However, for a 99.1% confidence level, the z-score will be higher because the tails are narrower. You would use a calculator, computer, or standard normal probability table to find z0.0045. In standard normal distribution tables or using a calculator's inverse normal function, z0.0045 corresponds to approximately zα/2 = 2.575. This is the critical value needed to construct your confidence interval.