Step 1 :We are given a cumulative area of 0.9808 under the standard normal distribution curve and we are asked to find the corresponding z-score.
Step 2 :The z-score is the number of standard deviations a given data point is from the mean.
Step 3 :We can use the inverse of the cumulative distribution function to find the z-score. The inverse of the cumulative distribution function gives the z-score that corresponds to a given cumulative area.
Step 4 :Using the inverse of the cumulative distribution function, we find that the z-score that corresponds to the cumulative area 0.9808 is approximately 2.07.
Step 5 :This means that a cumulative area of 0.9808 is 2.07 standard deviations above the mean in a standard normal distribution.
Step 6 :Final Answer: The z-score that corresponds to the cumulative area 0.9808 is approximately \(\boxed{2.07}\).