Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
standard deviation
a set of data has a mean of 12 and a standard deviation of 3. a data point of the set has a z-score of 1.3. what does a z-score of 1.3 mean?
the data point is 1.3 standard deviations away from 12.
the data point is 1.3 standard deviations away from 3.
the data point is 3 standard deviations away from 1.3.
the data point is 3 standard deviations away from 12.

Explanation:

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $z$ is the z - score, $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation. The z - score represents how many standard deviations a data point is away from the mean. Here, the mean ($\mu$) is 12 and the z - score is 1.3. So a z - score of 1.3 means the data point is 1.3 standard deviations away from the mean (12).

Answer:

The data point is 1.3 standard deviations away from 12.