Final answer:
The question involves z-scores and the area under the normal distribution curve, with areas to the left or right indicating proportions of the total curve. By using provided areas, one can locate corresponding z-scores using the Z-table.
Step-by-step explanation:
Understanding Z-Scores and Normal Distribution
The question refers to the concepts of z-scores and the normal distribution curve, which are part of statistics, a branch of mathematics. A z-score indicates how many standard deviations an element is from the mean. When we mention the area to the 'right' of a z-score, we are referring to the proportion of the total area under the normal distribution curve that is to the right of this z-score value. Conversely, the area to the 'left' of a z-score reflects the proportion of the total area under the curve to the left of the z-score value.
The problem provides various scenarios where you might need to find the z-score based on the cumulative area. For example, when the area to the right of z is 0.2206, we would look up the complement area (1 - 0.2206 = 0.7794) in the Z-table to find the associated z-score. In essence, you use the Z-table to identify the z-score that corresponds with a given area under the normal distribution curve.