Determine standard deviation from percentages

I have a normal distribution of data with a mean of 0. I know that 80% of the data falls within 3 units of the mean. So 80% of the data is from -3 to 3. How do I figure out the standard deviation? It's been a couple decades since my last math class and I'm forgetting this stuff. Thanks!


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You can find an answer based on what you've said but just so we know... do you or don't you have the data available to you?
I don't have the raw data. I've just been told that the data is a normal distribution and that 80% of the population is within 3 units of the mean. Do you know how to find the standard deviation from just this?


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Do you have an idea of what these data look like graphically (PDF)? Ideally, shouldn't 99% be within +/- 3 standard deviations?
Yes it's a normal distribution so 99% is within 3 standard deviations. My "3 units" description may be confusing. In my case the units is inches and I know that in my sample, 80% of the population's height is within 3" of the mean. I'm curious how to figure out the standard deviation from this type of data so I can apply it to other populations where I know X% of the population is within Y inches of the mean.