The value of z-score for a score that is three standard deviations above the mean is 3.
In this question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Let x be the score
let μ be the mean and
let σ be the standard deviations
Now, x = μ + 3σ
The formula of z-score is
[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]
⇒ [tex]z_{score} = 3[/tex]
Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.
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