Question

A score that is three standard deviations above the mean would have a z score of

Answer 1

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

$z_{score} = \frac{x-\mu}{\sigma}$

⇒ $z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}$

⇒ $z_{score} = \frac{ 3\sigma }{\sigma}$

⇒ $z_{score} = 3$

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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