Final answer:
The critical value zα/2 for an 87% confidence level is approximately 1.51, which is the z-score in the standard normal distribution that has an area of 0.065 to its right.
Step-by-step explanation:
To find the critical value zα/2 that corresponds to the given confidence level of 87%, we first determine the alpha level (α). Since the confidence level (CL) is 87% or 0.87, α = 1 - CL = 1 - 0.87 = 0.13.
Half of α (which is α/2) will be in each tail of the standard normal distribution, so α/2 = 0.065. The critical value zα/2 is the z-score that puts an area of 0.065 to its right in the standard normal distribution.
Using a standard normal probability table or statistical software, we find the z-score that corresponds to the area to the left as 1 - 0.065 = 0.935. The z-score that corresponds to this area to the left is approximately 1.51.
Therefore, zα/2 = 1.51 is our critical value for the 87% confidence interval.