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Which of the following graphs to the probability that z-score is between 0 and 1?

Which of the following graphs to the probability that z-score is between 0 and 1?-example-1
User Cyan
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1 Answer

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The z-score of a measure is given by the following formula


z=(x-\mu)/(\sigma)

where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.

If we have a z-score equal to zero, our measure will be


\begin{gathered} 0=(x-\mu)/(\sigma) \\ 0=x-\mu \\ x=\mu \end{gathered}

a z-score equal to zero represents the mean of the distribution.

For a z-score equal to 1, we have


\begin{gathered} 1=(x-\mu)/(\sigma) \\ \sigma=x-\mu \\ x=\mu+\sigma \end{gathered}

Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.


(\mu,\mu+\sigma)

The graph that represents this interval is the first graph.

User Alethea
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