Final answer:
The value of z for which the area to the right is 0.1314 is found by identifying the z-score that corresponds to an area of 0.8686 to the left on the z-table.
Step-by-step explanation:
The question is asking for the value of a z-score in a normal distribution, where the area to the right of z is 0.1314. This requires us to use a z-table or standard normal distribution table which maps z-scores to the area to the left of that score. Since the table provides the area to the left, we can find the area to the right by subtracting the area to the left from 1. In other words, we need to find a z that has an area of 1 - 0.1314 = 0.8686 to the left of it.
For example, if the z-table shows the area to the left of a z-score of 1 to be 0.1587, then the area to the right is 1 - 0.1587, which is approximately 0.8413. To find the exact z-score for an area of 0.8686 to the left, we would look at a z-table and find the closest value to 0.8686. Once we find it, we can identify the corresponding z-score, which is the value of z we are looking for.