Generate random number with normal distribution? I encountered this question, where given it is a normal distribution, how do we go about it to generate a series of random numbers beside Monte Carlo?
The clue given was using exponential function.
 A: Assuming you want to generate random numbers following the given normal distribution, a basic way would be to do Inverse Transform Sampling; the basic idea of which is to feed standard uniform random numbers to the inverse Cumulative Distribution Function (CDF), which in the case of a (for example standard) normal distribution is:
$ \Phi(x) = \frac{1}{\sqrt{2\pi}} \int_{- \infty}^{x} e ^ { \frac{-t^2}{2} } dt$
Now the CDF of the normal distribution does include an exponential function as your hint suggests. However, it is in the form of an intractable integral; meaning that it cannot be expressed by elementary functions and you should compute it with approximation methods. Besides, you would still have to compute the inverse of the above function. Take a look at Quantile function in the same Wikipedia page.
So if the discussion is more high-level and theory-driven, you can stop at the artificial closed form of the normal CDF and say "we feed standard uniform random numbers to the inverse of this function". But practically, you would have to tackle the integral with approximation methods\.
