Question

a set of data has a mean of 0.5 and a standard deviation of 0.01. a data point of the set has a z - score of 2.5. what does a z - score of 2.5 mean?
the data point is 0.01 standard deviations away from 2.5.
the data point is 0.01 standard deviations away from 0.5
the data point is 2.5 standard deviations away from 0.01
the data point is 2.5 standard deviations away from 0.5.

Explanation:

Step1: Recall z - score formula

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. It represents the number of standard deviations a data - point is away from the mean.

Step2: Interpret z - score value

Given a z - score of 2.5, $\mu = 0.5$ and $\sigma=0.01$. A z - score of 2.5 means that the data - point $x$ is 2.5 standard deviations away from the mean $\mu = 0.5$. The value of the standard deviation ($\sigma = 0.01$) is not the reference point for the z - score; the mean ($\mu = 0.5$) is. So the data point is 2.5 standard deviations away from 0.5.

Answer:

D. The data point is 2.5 standard deviations away from 0.5.