move test into test_seed_normal

Signed-off-by: Illia Sheshyn <187636533+illiasheshyn@users.noreply.github.com>

Author: illiasheshyn

mojo/stdlib/test/random/test_random.mojo

@@ -68,9 +68,12 @@ def test_random():
             ),
         )
 
+
+def test_seed_normal():
+    seed(42)
     # verify `randn_float64` values are normally distributed
-    var samples = List[Float64]()
-    var num_samples = 1_000_000
+    var num_samples = 1000
+    var samples = List[Float64](capacity=num_samples)
     for _ in range(num_samples):
         samples.append(randn_float64(0, 2))
 
@@ -82,31 +85,32 @@ def test_random():
 
     var sum_sq: Float64 = 0.0
     for sample in samples:
-        sum_sq += (sample[] - mean) * (sample[] - mean)
+        sum_sq += (sample[] - mean) ** 2
 
     var variance = sum_sq / num_samples
 
     # Calculate absolute differences (errors)
-    var mean_error = mean if mean > 0 else -mean
-    var variance_error = variance - 4 if variance > 4 else 4 - variance
+    var mean_error = abs(mean)
+    var variance_error = abs(variance - 4)
 
-    var tolerance: Float64 = 0.01
+    var mean_tolerance: Float64 = 0.06  # SE_μ = σ / √n
     assert_true(
-        mean_error < tolerance,
+        mean_error < mean_tolerance,
         String(
             "Mean error ",
             mean_error,
             " is above the accepted tolerance ",
-            tolerance,
+            mean_tolerance,
         ),
     )
+    var variance_tolerance: Float64 = 0.57  # SE_S² = √(2 * σ^4 / (n - 1))
     assert_true(
-        variance_error < tolerance,
+        variance_error < variance_tolerance,
         String(
             "Variance error ",
             variance_error,
             " is above the accepted tolerance ",
-            tolerance,
+            variance_tolerance,
         ),
     )