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:

Define the concept of a z-score

Using the Z-Score Formula knowledge point
A z-score measures the number of standard deviations a specific data point is away from the mean of the data set.

Interpret the given values

Using the Z-Score Formula knowledge point

• The mean of the data set is \(0.5\).
• The standard deviation is \(0.01\).
• The z-score of the data point is \(2.5\).

Apply the definition to the problem

Using the Z-Score Formula knowledge point
A z-score of \(2.5\) means that the data point is exactly \(2.5\) standard deviations away from the mean, which is \(0.5\).

Answer:

• 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. (Correct answer)