The negative z-score for an area of 0.1200 represents the distance below the mean, while the positive z-score for an area of 0.6400 represents the distance above the mean in a standard normal distribution.
The area under the curve of a negative z-score refers to the left tail of the standard normal distribution. To find the corresponding z-score for an area of 0.1200, one can look up this value in a standard normal distribution table or use a statistical calculator. The negative z-score indicates how many standard deviations the data point is below the mean. The result is a negative z-score, and its magnitude indicates the distance from the mean.
Similarly, for an area of 0.6400 under the curve of a positive z-score, this corresponds to the right tail of the standard normal distribution. Again, consulting a standard normal distribution table or using a statistical calculator will yield the positive z-score. The positive z-score indicates how many standard deviations the data point is above the mean.
In summary, for an area of 0.1200 under the curve of a negative z-score, the corresponding z-score represents the distance below the mean. For an area of 0.6400 under the curve of a positive z-score, the corresponding z-score represents the distance above the mean.