Two normal distributions are observed.The first distribution has a mean of 12 and a standard deviation of 2.The second distribution has a mean of 0 and a standard deviation of 2.For which distribution will the z score for the mean be larger?
A) the first z distribution
B) the second distribution
C) none, the z score will be the same

Question

Quizplus · Accepted Answer

The z-score for the mean of a distribution is always 0 because the z-score formula is $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value (in this case, the mean), $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the mean for $X$ results in a z-score of 0 for any distribution, regardless of its mean or standard deviation.

Two Normal Distributions Are Observed