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A set of data items is normally distributed with a mean of 90 and a standard deviation of 8. Convert 86 to a z-score.

A set of data items is normally distributed with a mean of 90 and a standard deviation-example-1
User Anirudhan J
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1 Answer

12 votes
12 votes

Step-by-step explanation

We are to find the z-score for the given data

To do so, we will use the formula:


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

where


\begin{gathered} x=observed\text{ mean=86} \\ \mu=90 \\ \sigma=8 \end{gathered}

Therefore,


\begin{gathered} z_(86)=(86-90)/(8)=-(4)/(8)=-0.5 \\ \\ z_(86)=-0.5 \end{gathered}

The z-score is -0.5

User Dan Mangiarelli
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