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.
This isn't the sort of thing you draw so much as generate.
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.
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.