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 concept

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: Interpret given z - score

Given a mean $\mu = 0.5$, standard deviation $\sigma=0.01$ and z - score $z = 2.5$. The z - score of 2.5 means the data point is 2.5 standard deviations away from the mean. Since the mean is 0.5, the data point is 2.5 standard deviations away from 0.5.

Answer:

The data point is 2.5 standard deviations away from 0.5