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Question

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. Convert each data item to a z-score. 100

Solution

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Given:

\begin{aligned} \text{Data value}&=100 \\ \text{Mean}&=60 \\ \text{Standard deviation}&=8 \end{aligned}

We need to determine the z-score corresponding to the data value.

The z-score is the difference between the data value and the mean, divided by the standard deviation.

\begin{aligned} z&=\frac{\text{Data value}-\text{Mean}}{\text{Standard deviation}} \end{aligned}

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