diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5ab93dd..55c7d96 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,8 @@
 # Changelog
 
+## 1.1.2 - 2024-12-14
+- Implementing `add()` method for NormalDist
+
 ## 1.1.1 - 2024-12-13
 - Implementing fromSample method for NormalDist
 
diff --git a/README.md b/README.md
index d6a3f53..33e145e 100644
--- a/README.md
+++ b/README.md
@@ -489,6 +489,7 @@ $normalDist = new NormalDist(float $mu = 0.0, float $sigma = 1.0);
 ### Methods
 
 #### Creating a normal distribution instance from sample data
+
 The `fromSamples()` static method creates a normal distribution instance with mu and sigma parameters estimated from the sample data.
 
 Example:
@@ -508,8 +509,8 @@ Calculates the **Probability Density Function** at a given value xxx:
 $normalDist->pdf(float $x): float
 ```
 
-**Input**: The value `$x` at which to evaluate the PDF.
-**Output**: The relative likelihood of `$x` in the distribution.
+- Input: the value `$x` at which to evaluate the PDF.
+- Output: the relative likelihood of `$x` in the distribution.
 
 Example:
 
@@ -527,8 +528,9 @@ 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`.
+- 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
@@ -536,9 +538,7 @@ $normalDist = new NormalDist(10.0, 2.0);
 echo $normalDist->cdf(12.0); // Output: 0.8413447460685429
 ```
 
-------
-
-### Use case example
+Calculating both, CDF and PDF:
 
 ```php
 $normalDist = new NormalDist(10.0, 2.0);
@@ -554,6 +554,29 @@ echo "CDF at x = 12: $cdf\n"; // Output: 0.8413447460685429
 
 ------
 
+#### Combining a normal distribution via `add()` method
+
+The `add()` method allows you to combine a NormalDist instance with either a constant or another NormalDist object.
+This operation supports mathematical transformations and the combination of distributions.
+
+The use cases are:
+- Shifting a distribution: add a constant to shift the mean, useful in translating data.
+- Combining distributions: combine independent or jointly normally distributed variables, commonly used in statistics and probability.
+
+```php
+$birth_weights = NormalDist::fromSamples([2.5, 3.1, 2.1, 2.4, 2.7, 3.5]);
+$drug_effects = new NormalDist(0.4, 0.15);
+$combined = $birth_weights->add($drug_effects);
+
+$combined->getMeanRounded(1); // 3.1
+$combined->getSigmaRounded(1); // 0.5
+
+$birth_weights->getMeanRounded(5); // 2.71667
+$birth_weights->getSigmaRounded(5); // 0.50761
+```
+
+------
+
 ### References for NormalDist
 
 This class is inspired by Python’s `statistics.NormalDist` and provides similar functionality for PHP users.
diff --git a/src/NormalDist.php b/src/NormalDist.php
index f1781ca..60ed114 100644
--- a/src/NormalDist.php
+++ b/src/NormalDist.php
@@ -111,5 +111,30 @@ public function cdfRounded(float $x, int $precision = 3): float
     }
 
 
+    /**
+     * Adds a constant or another NormalDist instance to this distribution.
+     *
+     * If the argument is:
+     * - A constant (float): Adjusts the mean (mu), leaving sigma unchanged.
+     * - A NormalDist instance: Combines the means and variances.
+     *
+     * @param float|NormalDist $x2 The value or NormalDist to add.
+     * @return NormalDist A new NormalDist instance with the updated parameters.
+     * @throws InvalidDataInputException If the argument is not a float or NormalDist.
+     */
+    public function add(float|NormalDist $x2): NormalDist
+    {
+        if ($x2 instanceof NormalDist) {
+            // Add the means and combine the variances (using the Pythagorean theorem)
+            $newMu = $this->mu + $x2->mu;
+            $newSigma = hypot($this->sigma, $x2->sigma);
+            // sqrt(sigma1^2 + sigma2^2)
+            return new NormalDist($newMu, $newSigma);
+        }
+        // Add a constant to the mean, sigma remains unchanged
+        return new NormalDist($this->mu + $x2, $this->sigma);
+    }
+
+
 
 }
diff --git a/tests/NormalDistTest.php b/tests/NormalDistTest.php
index 485d47d..50112e6 100644
--- a/tests/NormalDistTest.php
+++ b/tests/NormalDistTest.php
@@ -42,3 +42,25 @@
         $normalDist->getSigmaRounded(5),
     )->toEqual(0.50761);
 });
+
+
+it(' add to Normal Dist', function (): void {
+    $birth_weights = NormalDist::fromSamples([2.5, 3.1, 2.1, 2.4, 2.7, 3.5]);
+    $drug_effects = new NormalDist(0.4, 0.15);
+    $combined = $birth_weights->add($drug_effects);
+    expect(
+        $combined->getMeanRounded(1),
+    )->toEqual(3.1);
+    expect(
+        $combined->getSigmaRounded(1),
+    )->toEqual(0.5);
+
+    expect(
+        $birth_weights->getMeanRounded(5),
+    )->toEqual(2.71667);
+    expect(
+        $birth_weights->getSigmaRounded(5),
+    )->toEqual(0.50761);
+
+
+});