Question 15 A value \( X \) with a \( Z \) score of -1.5 is the mean.

If the standard deviation is 2, what is the value of \( X \)? To solve this problem, we can use the formula for the \( Z \) score: \[ Z = \frac{X - \mu}{\sigma} \] where: - \( Z \) is the \( Z \) score, - \( X \) is the value we want to find, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. Given that the \( Z \) score is -1.5, the mean \( \mu \) is the value \( X \) itself (since it's given as the mean), and the standard deviation \( \sigma \) is 2, we can plug these values into the formula and solve for \( X \): \[ -1.5 = \frac{X - X}{2} \] This simplifies to: \[ -1.5 = 0 \] This equation does not make sense because the left side is -1.5 and the right side is 0. It seems there might be a mistake in the problem statement. The \( Z \) score cannot be -1.5 if the mean \( X \) is the same as the value we are trying to find, because the \( Z \) score would then be 0. If the problem statement is correct, and the \( Z \) score is indeed -1.5, then the value of \( X \) would be the mean itself, which is not possible. Please check the problem statement again. If the mean \( X \) is not the value we are trying to find, please provide the correct information so we can solve the problem.