Final answer:
Whenever a data value is less than the mean, the corresponding z-score is negative. The z-score indicates the number of standard deviations a data point is below the mean. The correct answer is D.
Step-by-step explanation:
Whenever a data value is less than the mean, the corresponding z-score is negative. A z-score represents how many standard deviations away a data point is from the mean of the data set. A positive z-score indicates that the data value is above the mean, while a negative z-score suggests it is below the mean.
For example, if we have a data value, x = 1, and a mean, μ = 5, and find that the z-score is -0.67, this signifies that x is 0.67 standard deviations below the mean. This context implies that the data value doesn't deviate too far below the mean, as it is less than one standard deviation away.
Further, in a normal distribution, approximately 68% of data falls between z-scores of -1 and 1, about 95% between -2 and 2, and around 99.7% between -3 and 3, according to the empirical rule, also known as the 68-95-99.7 rule. The z-score directly indicates the distance and direction of a data value from the mean, with relation to standard deviation.