If the standard normal deviate of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2, then the mean of x is:
A) 6
B) 4
C) 8
D) 2
E) 0

Question

Quizplus · Accepted Answer

The standard normal deviate (z-score) is calculated as $z = \frac{x - \mu}{\sigma}$, where $x$ is the value of the random variable, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $z = -2$, $x = 2$, and $\sigma = 2$, we can solve for $\mu$: $-2 = \frac{2 - \mu}{2}$. Solving for $\mu$ gives $\mu = 6$.

If the Standard Normal Deviate of a Random Variable Value