Which of the following statements are TRUE about the normal distribution? Check all that apply.
a. A z-score is the number of standard deviations a specific data value is from the mean of the distribution.
b. The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.
c. A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.
d. The mean corresponds to the z-score of 1.
e. The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Hence, only statement D is false, as the mean corresponds to z-score of 0.

More can be learned about the normal distribution at https://brainly.com/question/24663213