diff --git a/CHANGELOG.md b/CHANGELOG.md
index d8e24fd..59d174f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,7 +1,7 @@
 # Changelog
 
-## 1.0.2 - WIP
-
+## 1.0.2 - 2024-12-10
+- NormalDist class, with `cdf()` and `pdf()`
 - Fix deprecations for PHP 8.4
 
 ## 1.0.1 - 2024-11-21
diff --git a/README.md b/README.md
index e529fc9..797b6d9 100644
--- a/README.md
+++ b/README.md
@@ -462,6 +462,92 @@ Array
  */
 
 ```
+## `NormalDist` class
+
+The `NormalDist` class provides an easy way to work with normal distributions in PHP. It allows you to calculate probabilities and densities for a given mean (μ\muμ) and standard deviation (σ\sigmaσ).
+
+### Key features
+
+- Define a normal distribution with mean (μ\muμ) and standard deviation (σ\sigmaσ).
+- Calculate the **Probability Density Function (PDF)** to evaluate the relative likelihood of a value.
+- Calculate the **Cumulative Distribution Function (CDF)** to determine the probability of a value or lower.
+
+------
+
+### Class constructor
+
+```php
+$normalDist = new NormalDist(float $mu = 0.0, float $sigma = 1.0);
+```
+
+- `$mu`: The mean (default = `0.0`).
+- `$sigma`: The standard deviation (default = `1.0`).
+- Throws an exception if `$sigma` is non-positive.
+
+------
+
+### Methods
+
+#### 1. `pdf($x)`
+
+Calculates the **Probability Density Function** at a given value xxx:
+
+```php
+$normalDist->pdf(float $x): float
+```
+
+**Input**: The value `$x` at which to evaluate the PDF.
+**Output**: The relative likelihood of `$x` in the distribution.
+
+Example:
+
+```php
+$normalDist = new NormalDist(10.0, 2.0);
+echo $normalDist->pdf(12.0); // Output: 0.12098536225957168
+```
+
+------
+
+#### 2. `cdf($x)`
+
+Calculates the **Cumulative Distribution Function** at a given value `$x`:
+
+```php
+$normalDist->cdf(float $x): float
+```
+**Input**: The value `$x` at which to evaluate the CDF.
+**Output**: The probability that a random variable `$x` is less than or equal to `$x`.
+Example:
+
+```php
+$normalDist = new NormalDist(10.0, 2.0);
+echo $normalDist->cdf(12.0); // Output: 0.8413447460685429
+```
+
+------
+
+### Use case example
+
+```php
+$normalDist = new NormalDist(10.0, 2.0);
+
+// Calculate PDF at x = 12
+$pdf = $normalDist->pdf(12.0);
+echo "PDF at x = 12: $pdf\n"; // Output: 0.12098536225957168
+
+// Calculate CDF at x = 12
+$cdf = $normalDist->cdf(12.0);
+echo "CDF at x = 12: $cdf\n"; // Output: 0.8413447460685429
+```
+
+------
+
+### References for NormalDist
+
+This class is inspired by Python’s `statistics.NormalDist` and provides similar functionality for PHP users.
+
+
+
 ## Testing
 
 ```bash
diff --git a/src/NormalDist.php b/src/NormalDist.php
new file mode 100644
index 0000000..81488dc
--- /dev/null
+++ b/src/NormalDist.php
@@ -0,0 +1,82 @@
+<?php
+
+namespace HiFolks\Statistics;
+
+use HiFolks\Statistics\Exception\InvalidDataInputException;
+
+class NormalDist
+{
+    // Mean
+
+    private readonly float $sigma; // Standard deviation
+
+    // Constructor to initialize mu and sigma
+    public function __construct(private readonly float $mu = 0.0, float $sigma = 1.0)
+    {
+        if ($sigma < 0) {
+            throw new InvalidDataInputException('Standard deviation (sigma) cannot be negative.');
+        }
+        $this->sigma = $sigma;
+    }
+
+    // Getter for mean (read-only)
+    public function getMean(): float
+    {
+        return $this->mu;
+    }
+
+    // Getter for standard deviation (read-only)
+    public function getSigma(): float
+    {
+        return $this->sigma;
+    }
+
+    // A utility function to calculate the probability density function (PDF)
+    public function pdf(float $x): float
+    {
+        $coeff = 1 / (sqrt(2 * M_PI) * $this->sigma);
+        $exponent = -($x - $this->mu) ** 2 / (2 * $this->sigma ** 2);
+
+        return $coeff * exp($exponent);
+    }
+
+    public function pdfRounded(float $x, int $precision = 3): float
+    {
+        return round($this->pdf($x), $precision);
+    }
+
+    // Approximate the error function (erf)
+    private function erf(float $z): float
+    {
+        $t = 1 / (1 + 0.5 * abs($z));
+        $tau = $t * exp(-$z * $z
+                - 1.26551223
+                + 1.00002368 * $t
+                + 0.37409196 * $t ** 2
+                + 0.09678418 * $t ** 3
+                - 0.18628806 * $t ** 4
+                + 0.27886807 * $t ** 5
+                - 1.13520398 * $t ** 6
+                + 1.48851587 * $t ** 7
+                - 0.82215223 * $t ** 8
+                + 0.17087277 * $t ** 9);
+        return $z >= 0 ? 1 - $tau : $tau - 1;
+    }
+
+
+    // A utility function to calculate the cumulative density function (CDF)
+    public function cdf(float $x): float
+    {
+        $z = ($x - $this->mu) / ($this->sigma * sqrt(2));
+
+        return 0.5 * (1 + $this->erf($z));
+    }
+
+    public function cdfRounded(float $x, int $precision = 3): float
+    {
+        return round($this->cdf($x), $precision);
+    }
+
+
+
+}
diff --git a/tests/NormalDistTest.php b/tests/NormalDistTest.php
new file mode 100644
index 0000000..dbee801
--- /dev/null
+++ b/tests/NormalDistTest.php
@@ -0,0 +1,30 @@
+<?php
+
+use HiFolks\Statistics\NormalDist;
+
+it(' init normal dist', function (): void {
+    $nd = new NormalDist(1060, 195);
+    expect(
+        $nd->getMean(),
+    )->toEqual(1060);
+    expect(
+        $nd->getSigma(),
+    )->toEqual(195);
+
+});
+it('can calculate normal dist cdf', function (): void {
+    $nd = new NormalDist(1060, 195);
+    expect(
+        round($nd->cdf(1200 + 0.5) - $nd->cdf(1100 - 0.5), 3),
+    )->toEqual(0.184);
+});
+
+it('can calculate normal dist pdf', function (): void {
+    $nd = new NormalDist(10, 2);
+    expect(
+        $nd->pdfRounded(12, 3),
+    )->toEqual(0.121);
+    expect(
+        $nd->pdfRounded(12, 2),
+    )->toEqual(0.12);
+});