Normal areas from math.erf

You will write the standard normal area $\Phi(z)$ from math.erf, use it for the share between two values of any normal distribution, and work out the share within $k$ standard deviations. The checker compares your answers with statistics.NormalDist.

The idea. $\Phi(z) = \dfrac{1}{2}\left(1 + \text{erf}\left(\dfrac{z}{\sqrt{2}}\right)\right)$. For any normal distribution, turn each value into a z-score first, then take one area from the other.

Your tasks.

1. Finish phi(z).
2. Finish area_between(low, high, mean, sd). Use z-scores and phi.
3. Finish within(k), the share within k standard deviations of the mean.