diff --git a/mlx/random.cpp b/mlx/random.cpp
index 63e39cdcc..5e0682d32 100644
--- a/mlx/random.cpp
+++ b/mlx/random.cpp
@@ -153,14 +153,23 @@ array uniform(
 array normal(
     const std::vector<int>& shape,
     Dtype dtype,
+    const float loc /* = 0.0 */,
+    const float scale /* = 1.0 */,
     const std::optional<array>& key /*= nullopt */,
     StreamOrDevice s /* = {} */) {
   auto stream = to_stream(s);
   auto low = array(std::nextafter(-1.0f, 0.0f), dtype);
   auto high = array(1.0f, dtype);
   auto samples = uniform(low, high, shape, dtype, key, stream);
-  return multiply(
-      array(std::sqrt(2.0), dtype), erfinv(samples, stream), stream);
+  samples =
+      multiply(array(std::sqrt(2.0), dtype), erfinv(samples, stream), stream);
+  if (scale != 1.0) {
+    samples = multiply(array(scale, dtype), samples, stream);
+  }
+  if (loc != 0.0) {
+    samples = add(array(loc, dtype), samples, stream);
+  }
+  return samples;
 }
 
 array randint(
diff --git a/mlx/random.h b/mlx/random.h
index ab75eb488..1397b32d7 100644
--- a/mlx/random.h
+++ b/mlx/random.h
@@ -95,13 +95,30 @@ inline array uniform(
 array normal(
     const std::vector<int>& shape,
     Dtype dtype,
+    const float loc,
+    const float scale,
     const std::optional<array>& key = std::nullopt,
     StreamOrDevice s = {});
 inline array normal(
     const std::vector<int>& shape,
+    const float loc,
+    const float scale,
     const std::optional<array>& key = std::nullopt,
     StreamOrDevice s = {}) {
-  return normal(shape, float32, key, s);
+  return normal(shape, float32, loc, scale, key, s);
+}
+inline array normal(
+    const std::vector<int>& shape,
+    const Dtype dtype,
+    const std::optional<array>& key = std::nullopt,
+    StreamOrDevice s = {}) {
+  return normal(shape, dtype, 0.0, 1.0, key, s);
+}
+inline array normal(
+    const std::vector<int>& shape,
+    const std::optional<array>& key = std::nullopt,
+    StreamOrDevice s = {}) {
+  return normal(shape, float32, 0.0, 1.0, key, s);
 }
 
 /** Generate integer samples uniformly at random */
diff --git a/python/src/random.cpp b/python/src/random.cpp
index 6e9f38d97..e9140e7d9 100644
--- a/python/src/random.cpp
+++ b/python/src/random.cpp
@@ -99,13 +99,17 @@ void init_random(py::module_& parent_module) {
       "normal",
       [](const std::vector<int>& shape,
          std::optional<Dtype> type,
+         float loc,
+         float scale,
          const std::optional<array>& key,
          StreamOrDevice s) {
-        return normal(shape, type.value_or(float32), key, s);
+        return normal(shape, type.value_or(float32), loc, scale, key, s);
       },
 
       "shape"_a = std::vector<int>{},
       "dtype"_a = std::optional{float32},
+      "loc"_a = 0.0,
+      "scale"_a = 1.0,
       "key"_a = none,
       "stream"_a = none,
       R"pbdoc(
@@ -114,6 +118,8 @@ void init_random(py::module_& parent_module) {
         Args:
             shape (list(int), optional): Shape of the output. Default is ``()``.
             dtype (Dtype, optional): Type of the output. Default is ``float32``.
+            loc (float, optional): Mean of the distribution. Default is ``0.0``.
+            scale (float, optional): Standard deviation of the distribution. Default is ``1.0``.
             key (array, optional): A PRNG key. Default: None.
 
         Returns:
diff --git a/python/tests/test_random.py b/python/tests/test_random.py
index 0a06c3496..892db37df 100644
--- a/python/tests/test_random.py
+++ b/python/tests/test_random.py
@@ -80,6 +80,20 @@ class TestRandom(mlx_tests.MLXTestCase):
             a = mx.random.normal(dtype=t)
             self.assertEqual(a.dtype, t)
 
+        # Generate with a given mean and standard deviation
+        loc = 1.0
+        scale = 2.0
+
+        a = mx.random.normal(shape=(3, 2), loc=loc, scale=scale, key=key)
+        b = scale * mx.random.normal(shape=(3, 2), key=key) + loc
+        self.assertTrue(mx.allclose(a, b))
+
+        a = mx.random.normal(
+            shape=(3, 2), loc=loc, scale=scale, dtype=mx.float16, key=key
+        )
+        b = scale * mx.random.normal(shape=(3, 2), dtype=mx.float16, key=key) + loc
+        self.assertTrue(mx.allclose(a, b))
+
         self.assertEqual(mx.random.normal().dtype, mx.random.normal(dtype=None).dtype)
 
     def test_randint(self):