Given the mean score of a group of people in a quiz, the standard deviation of the scores of the people, and the score of a person, we can easily determine the z-score like this:
[tex]z=\frac{x-μ}{σ}[/tex]
Where σ is the standard deviation, μ is the mean score and x is the score. By replacing 78 for μ, 4.2 for σ and 80 for x, we get:
[tex]z=\frac{80-78}{4.2}=0.4762[/tex]
Then the z-score equals 0.4762. In this case, the score of 80 is a usual value since it is within one standard deviation of the mean.
