z-scores and the bands

You will write three functions. The first turns a list into z-scores. The second finds the share of values within $k$ standard deviations. The third turns a z-score back into a value. Use the population SD, statistics.pstdev.

The idea. $z = \dfrac{x - \text{mean}}{\text{SD}}$. A value is within $k$ SDs when $|z| \le k$. Going back, $x = \text{mean} + z \times \text{SD}$.

Your tasks.

1. Finish z_scores(data). Return the list of z-scores.
2. Finish share_within(data, k). Return the fraction of values with $|z| \le k$.
3. Finish value_from_z(z, mean, sd).