The integral of this function, the error function, allows one to calculate (*) probabilities based on z-scores, which represent the number of standard deviations away from the mean of this distribution.
The Box-Mueller transformation converts a uniform distribution to this distribution. If the sum of two random variables has this distribution, then both of those random variables have this distribution by Cramer's Theorem. The distribution of sample means of any distribution converges to this distribution by the Central Limit Theorem. The integral of this function, the error function, allows one to calculate (*) probabilities based on z-scores, which represent the number of standard deviations away from the mean of this distribution. For 10 points, name this distribution that resembles a bell curve.
The Box-Mueller transformation converts a uniform distribution to this distribution.
{normal} distribution [or {Gaussian} distribution; prompt on {bell curve}]