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:

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 $\mu = 0.5$ and the z - score is 2.5. So a z - score of 2.5 means the data point is 2.5 standard deviations away from the mean (0.5). We can eliminate the other options: the first option is incorrect as it misinterprets the relationship between the z - score, standard deviation, and the value 2.5; the second option uses the wrong number of standard deviations (0.01 instead of 2.5); the third option uses the wrong reference (0.01 instead of the mean 0.5).

Answer:

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