Final answer:
The critical probability for a 58% confidence level is 0.21, representing the area in one tail of the normal distribution, as the central 58% is covered by the confidence level, leaving 21% in each tail.
Step-by-step explanation:
When finding the margin of error for a mean from a sample with a confidence level of 58%, the critical probability would be at the point where the central 58% of the distribution is covered. This leaves 42% in the tails (100%–58%). Since the normal distribution is symmetric, you will have 21% in each tail (42%/2). Therefore, the critical probability, that is, the area in one tail for a 58% confidence level, is 0.21. To find the z-score corresponding to this area in the tail, we would look up the area (0.5 + 0.21 = 0.71) in the body of a z-table to find the z-score that corresponds to this cumulative probability.
However, this process is not necessary to answer the question directly, as the critical probability is specifically the area in one tail for the given confidence level, not the z-score itself. The critical probability for a confidence level of 58% can be calculated by subtracting the confidence level from 1. Since the confidence level is 58%, the critical probability would be 1 minus 0.58 = 0.42. Therefore, option b, 0.42, would be the correct choice.