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…
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?\nthe data point is 1.3 standard deviations away from 3\nthe data point is 1.3 standard deviations away from 12.\nthe data point is 3 standard deviations away from 1.3.\nthe data point is 3 standard deviations away from 12.
Answer
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 z - score
Given a 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 $\mu$. Since $\mu = 12$, the data point is 1.3 standard deviations away from 12.
Answer:
The data point is 1.3 standard deviations away from 12.