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?\no the data point is 0.01 standard deviations away from 2.5.\no the data point is 0.01 standard deviations away from 0.5\no the data point is 2.5 standard deviations away from 0.01.\no the data point is 2.5 standard deviations away from 0.5.
Answer
Explanation:
Step1: Recall z - score formula concept
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. A z - score represents the number of standard deviations a data point is from the mean.
Step2: Interpret given z - score
Given a z - score of 2.5, the mean $\mu = 0.5$, and standard deviation $\sigma=0.01$. The z - score of 2.5 means the data point is 2.5 standard deviations away from the mean. The mean is 0.5.
Answer:
The data point is 2.5 standard deviations away from 0.5.