Biostats Question (Z Score)

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seminoma

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So in a normal distribution, a +/- 1 SD covers 68% of all the data and a zscore of +1 equates to the point at which 84% of the data is covered (i.e. the 84th percentile). What happens if the data is skewed? For example, if the data is negatively skewed, does a zscore of +1 now mean something less than the 84th percentile?
 
The distribution doesn't matter. It's just a way of making another distribution. When the data is skewed, the standard deviation will just change.
 
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