Question

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 3 the data point is 1.3 standard deviations away from 12 the data point is 3 standard deviations away from 1.3 the data point is 3 standard deviations away from 12.

Explanation:

Step1: Recall z - score definition

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation. A z - score represents the number of standard deviations a data point is from the mean.

Step2: Analyze given values

Here, the mean $\mu = 12$, standard deviation $\sigma=3$, and z - score $z = 1.3$. A z - score of 1.3 means the data point $x$ is 1.3 standard deviations away from the mean value of 12.

Answer:

The data point is 1.3 standard deviations away from 12.