To find the critical value zα/2 for a 91% confidence level, we first need to determine the value of α (alpha). The confidence level of 91% implies that α = 1 – 0.91 = 0.09. Since we are looking for zα/2, we need to find α/2, which is 0.09/2 = 0.045.
Next, we will refer to the standard normal (Z) distribution table or a calculator to find the z-score that corresponds to the cumulative probability of 1 – 0.045 = 0.955. This is because we are looking for the z-value that leaves 4.5% in the upper tail.
Using the Z-table or calculator, we find that the critical value that corresponds to an area of 0.955 is approximately 1.645.
Therefore, the critical value zα/2 for a 91% confidence level is:
zα/2 = 1.645