Final answer:
The critical value Zα/2 corresponding to α = 0.20 in a standard normal distribution is 1.28, which means that the area to the left of Zα/2 (1.28) is 0.90, leaving 10% in the right tail.
Step-by-step explanation:
The question pertains to finding the critical value Zα/2 for a standard normal distribution when α equals 0.20. In a standard normal distribution, the critical value is a point on the z-score scale that represents a specified level or probability, effectively splitting the tail areas of the distribution. For a two-tailed test with α = 0.20, we are interested in the critical values that leave 10% in each tail, since α/2 = 0.10.
Using probability tables or a calculator that provides normal distribution probabilities or percentiles, we can determine that the Zα/2 value leaving an area of 0.10 in the right tail, and hence an area of 0.90 to the left, is approximately 1.28. Therefore, the critical value Z0.10 is 1.28. This value represents a z-score on a standard normal distribution where the area under the curve to the left of 1.28 is 0.90, or 90% of the distribution is contained within ±1.28 standard deviations from the mean.
Based on this, the corresponding Zα/2 value for α = 0.20 is 1.28, and the correct answer to the provided options is: a) Z0.20/2 = 1.28.