input: def predict_customer_lifetime_value(transactions_file: str, customer_input: np.ndarray) -> float:
      """ Predicts the customer lifetime value (LTV) given a customer's past transactions.
      The model uses a RandomForestRegressor after preprocessing the data with StandardScaler.
      
      >>> predict_customer_lifetime_value('transactions.csv', np.array([[10, 100, 5]]))
      'Predicted customer lifetime value: 1234.56'  # Example output
      >>> predict_customer_lifetime_value('transactions.csv', np.array([[5, 50, 2]]))
      'Predicted customer lifetime value: 789.01'  # Example output
      """
output:     
      import pandas as pd
      from sklearn.ensemble import RandomForestRegressor
      from sklearn.preprocessing import StandardScaler
      from sklearn.model_selection import train_test_split
  
      # Load the transactions data
      df = pd.read_csv(transactions_file)
      
      # Preprocess the data
      X = df.drop('lifetime_value', axis=1)
      y = df['lifetime_value']
      scaler = StandardScaler()
      X_scaled = scaler.fit_transform(X)
      
      # Train the model
      X_train, _, y_train, _ = train_test_split(X_scaled, y, test_size=0.2, random_state=42)
      model = RandomForestRegressor(random_state=42)
      model.fit(X_train, y_train)
      
      # Predict the customer lifetime value
      customer_input_scaled = scaler.transform(customer_input)
      prediction = model.predict(customer_input_scaled)
      
      return f'Predicted customer lifetime value: {prediction[0]:.2f}'
  