Question
Assume the mean \( =100 \) and the standard deviation \( =25: x=60, z= \)
Ask by Brewer Bartlett.
Jan 25,2025 03:18
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Answer
The z-score for \( x = 60 \) is **-1.6**.
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To find the z-score, you can use the formula: \( z = \frac{(x - \mu)}{\sigma} \). Plugging in the values: \( z = \frac{(60 - 100)}{25} = \frac{-40}{25} = -1.6 \). So, the z-score for \( x = 60 \) is \(-1.6\). This means that 60 is 1.6 standard deviations below the mean.
In practical terms, z-scores help to understand how far a data point is from the average relative to the variation in the dataset. A z-score of -1.6 indicates that 60 is less than the average value of 100, which can be a signal to investigate why that measurement is lower – perhaps it signifies an anomaly or a unique situation.
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