Which of the following statements is true regarding \( z \)-scores for the normal probability distribution? \( z \)-scores are equal to 1.0 for values of \( x \) that are equal to the distribution mean. \( z \)-scores are zero for a value of \( x \) that is less than the distribution mean. \( z \)-scores are positive for values of \( x \) that are less than the distribution mean. \( z \) negative for values of \( x \) that are less than the distribution mean.

The \( z \)-score is defined as \[ z = \frac{x - \mu}{\sigma} \] where: - \( \mu \) is the mean of the distribution, - \( \sigma \) is the standard deviation, - \( x \) is the value being standardized. 1. For a value of \( x \) equal to the distribution mean, \( \mu \), the calculation is \[ z = \frac{\mu - \mu}{\sigma} = \frac{0}{\sigma} = 0. \] Therefore, the statement "\( z \)-scores are equal to 1.0 for values of \( x \) that are equal to the distribution mean" is false. 2. For a value of \( x \) less than the distribution mean, \( \mu \), the numerator \( (x - \mu) \) is negative, which makes \( z \) negative. Thus, stating that "\( z \)-scores are zero for a value of \( x \) that is less than the distribution mean" or that "\( z \)-scores are positive for values of \( x \) that are less than the distribution mean" is incorrect. 3. The correct statement is that \( z \) is negative for values of \( x \) that are less than the distribution mean. Thus, the true statement is: \( z \) negative for values of \( x \) that are less than the distribution mean.