A z score of 2.66 means that the raw score in question is ________ the mean of the distribution.

Explanation
d is correct
Z score helps in knowing whether the obtained raw score values are below or above the standard mean.

Z score of positive 2.66 implies that the raw score is 2.66 deviations above the mean in the distribution.

a is incorrect
Z score is measured by subtracting the mean of the scores from the observed score and dividing it by the standard deviation of the scores. It helps one to know the probability value in the distribution and also helps one to compare two values from different distributions.

If the z score is 2.66, it does not mean that the raw score would be 1.33 standard deviations below the mean score.

b is incorrect
Z score is also known as the standard score as it gives an idea about the standard deviation above and below the mean value. It is useful in statistics as it allows one to calculate the standard deviation across a normal distribution by calculating a single value.

A z score of 2.66 does not imply that the raw score is 1.33 standard deviations above the mean.

c is incorrect
Deriving a standard score is the statistical method of determining the raw value of the set of scores, and how it is above or below the mean value.

Having a z score of 2.66 does not equate to having a raw score of 2.66 standard deviations above the mean.