z_table 0.1.3

Provides lookup functions for the standard normal table, also called Z table.
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# 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. The error is roughly 0.1%.

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
```