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…

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?\nthe data point is 0.01 standard deviations away from 2.5.\nthe data point is 0.01 standard deviations away from 0.5.\nthe data point is 2.5 standard deviations away from 0.01.\nthe data point is 2.5 standard deviations away from 0.5.

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?\nthe data point is 0.01 standard deviations away from 2.5.\nthe data point is 0.01 standard deviations away from 0.5.\nthe data point is 2.5 standard deviations away from 0.01.\nthe data point is 2.5 standard deviations away from 0.5.

Answer

Answer:

The data point is 2.5 standard deviations away from 0.5.

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

Here, the mean $\mu = 0.5$, the standard deviation $\sigma=0.01$, and the z - score $z = 2.5$. By the definition of the z - score, a z - score of 2.5 means the data point is 2.5 standard deviations away from the mean value of 0.5.