I tried to draw like this picture but failed. I used Dia.
What can I use to help draw it? I'm using Ubuntu, so software that runs on Unix operating systems would be preferred.
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You could draw it with any vector app (such as Joonas' Inkscape recommendation). But, you're probably looking for something with better mathematical accuracy than that.
I think what you're after is something generated by a computational app. You could export the generated graphic to style in Inkscape, if you wanted to embellish/annotate it. I've been provided with such graphics but I've never had to build them myself. Hopefully someone will chime in with a recommendation.
You could try with GeoGebra.
GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package.
The Mathematics SE site has quite a few similar questions you might find useful. A search for "graphing" and "bell curves" might take you to one that can help. If you can't find any, we can migrate this question to them.