I need to generate normal random floats in range [0;1], but randn(Float64) uses a different range.
How to fix it?
The normal distribution has infinite support (in theory). randn samples a normal distribution with variance 1 and mean 0 (so most values are in [-1, 1] and very few values are outside [-5, 5]). If you want to reshape this, you can always add and multiply: almost all outputs of randn()/5 + 0.5 will be in your suggested range.
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In the normal distribution, most values are within [-0.6744897501960818, 0.6744897501960818]… 
If you sample from a distribution but throw away any values outside a range, you effectively sample a truncated distribution. I must emphasize that a truncated distribution is not the same as the original distribution, but it’s what you use if you really need a strict range. Distributions.jl supports truncation of univariate distributions, and you use rand to sample. As @gustaphe said, you could truncate to [-a, a] and adjust the values to the range [0, 1], or you could also adjust the mean and variance of the Normal distribution before you truncate it to [0, 1].
Both statements are true 
.
I normally go by the 68-95-99.7 rule, but I never remember the specific numbers so I call it “most”, “almost all”, “pretty much all”.
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