# Z-Score

The z-score represents number of Standard Deviations above or below that $X$ is from mean $μ$.

If a Z-score is $0$, it indicates that our data point(s) $X$ is identical to the mean score. $Z=σX−μ $

### Z-Table

Mapping value to probability.

Ahh, so if you Z-score is 0, you see that the probability is exactly 50%, which makes sense, because the distribution is centered around $0$.

The Quantiles, this is just a reverse mapping of probability to original value.

### Some Examples

It really helps if you draw the area under the distribution.

- $P(Z≥1)=1−0.84134$
- $P(Z≥−1.2)=P(Z≤1.2)=0.88493$
- $P(Z≤−0.7)=1−P(Z≤0.7)=1−0.75804$
- $P(1≤Z≤2)=P(Z≤2)−P(Z≤1)=0.97725−0.84134$