if a data value in a normal distribution has a negative z - score, which of the following must be true? the…
if a data value in a normal distribution has a negative z - score, which of the following must be true? the data value must be negative. the data value must be positive. the data value must be less than the mean. the data value must be greater than the mean.
Answer
Brief Explanations:
The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - value, $\mu$ is the mean and $\sigma$ is the standard deviation. Since $\sigma>0$, if $z<0$, then $x-\mu<0$, which implies $x < \mu$. The sign of the data - value itself is not determined by the sign of the z - score.
Answer:
The data value must be less than the mean.