# Z Table
This crate provides lookup functions for the standard normal table, also called Z table. Because the lookup functions are `const fn`, they can be evaluated at compile time. This crate is:
* **Small** in size
* **Fast**, as it relies on simple table lookups and can be evaluated at compile time
* **Minimalistic**, only some basic table lookup functions are provided
Keep in mind that this crate isn't the most precise as it only relies on table lookups.
If you need something more precise with more functionaliy, don't use this crate. An alternative would be [statrs](https://crates.io/crates/statrs).
## Example
```rust
use z_table::{lookup_with, reverse_lookup_with};
fn main() {
// Some birth weights of newborns in kg.
let birth_weights: [f32; 5] = [2.5, 2.7, 3.1, 3.4, 3.6];
let n = birth_weights.len() as f32;
// Calculate the average weight of a newborn.
let mean: f32 = birth_weights.iter().sum::<f32>() / n;
// Calculate the variance and standard derivation.
let variance: f32 = birth_weights.iter().map(|x| x.powi(2)).sum::<f32>() / n - mean.powi(2);
let standard_derivation = variance.sqrt();
println!(
"The probability of a newborn to weight less than 3.5 kg is {} %",
lookup_with(3.5, mean, standard_derivation) * 100.0
);
println!(
"The weight of a newborn is with a 90 % probability under {} kg",
reverse_lookup_with(0.9, mean, standard_derivation)
);
}
```
The output is:
```text
The probability of a newborn to weight less than 3.5 kg is 85.54277 %
The weight of a newborn is with a 90 % probability under 3.588379 kg
```