Final answer:
To construct a 95% confidence interval, we find the critical value zα/2 from the standard normal distribution. The critical value for a 95% confidence level is zα/2 = 1.96, which is the z-score with 0.025 in each of the distribution's tails.
Step-by-step explanation:
To find the critical value zα/2 necessary to construct a 95% confidence interval, we must consider the standard normal distribution. For a 95% confidence interval, the area in the middle of the distribution (CL), which represents the confidence level, is 95%. This is the area between the two critical z-scores that we are looking for. The confidence level (CL) can be represented as CL = 1 - α, where α is the sum of the areas in both tails of the distribution. Since 95% is the area in the middle, α = 0.05, dividing equally to 0.025 in each tail of the distribution.
Using a standard normal probability table or calculator, we look up the z-score that corresponds to an area of 0.975 (which is 1 - 0.025), since the z-score will be the point where there is 2.5% in the tail beyond it. The z-score that corresponds to this is zα/2 = 1.96. This is the critical value needed to construct our 95% confidence interval.