if a data value in a normal distribution has a negative z - score, which of the following must be true?\nthe…
if a data value in a normal distribution has a negative z - score, which of the following must be true?\nthe data value must be negative.\nthe data value must be positive.\nthe data value must be less than the mean.\nthe data value must be greater than the mean.
Answer
Brief Explanations:
The formula for the z - score 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 $x < \mu$. A negative z - score means the data value is below the mean, and the data value itself can be positive or negative.
Answer:
The data value must be less than the mean.