Creating a random point under the standard distribution curv

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The random function in programming languages creates a (pseudo-)random number that has an equal chance of being anywhere in the range 0.0 to 1.0. For example if the mean was 0.0 and a "standard deviation" was 1.0, the random number could be anything. However, it would be more likely to lie between 0 and 1 than between 1 and 2 and a number > 5 would be extremely unlikely (previous integers could also be negative ending in ... < -5).

Thanks in advance.

It wouldn't be able to be a non-computable number, though. So it couldn't be just ANY number, right?

What I came up with ran the random function 20 times, summing the results. Applying the appropriate tweaks to it, I get a range of between -7.77 and + 7.77. Not exactly what I wanted but good enough "for all practical purposes".