input: Write a python function to create, compile, and train a neural network model using Keras and evaluate its performance.
  assert isinstance(create_and_train_model(np.random.rand(100, 5), np.random.randint(2, size=100)), dict)
  assert 'score' in create_and_train_model(np.random.rand(100, 5), np.random.randint(2, size=100))
  assert 'accuracy' in create_and_train_model(np.random.rand(100, 5), np.random.randint(2, size=100))
output: def create_and_train_model(X, y):
      from keras.models import Sequential
      from keras.layers import Dense
      from keras.optimizers import Adam
      from sklearn.model_selection import train_test_split
      from sklearn.preprocessing import StandardScaler
  
      # Split the data into training and testing sets
      X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
  
      # Standardize the data
      scaler = StandardScaler()
      X_train = scaler.fit_transform(X_train)
      X_test = scaler.transform(X_test)
  
      # Create the model
      model = Sequential()
      model.add(Dense(64, input_dim=X_train.shape[1], activation='relu'))
      model.add(Dense(32, activation='relu'))
      model.add(Dense(1, activation='sigmoid'))
  
      # Compile the model
      model.compile(optimizer=Adam(), loss='binary_crossentropy', metrics=['accuracy'])
  
      # Train the model
      model.fit(X_train, y_train, epochs=50, batch_size=10, verbose=0)
  
      # Evaluate the model
      score, accuracy = model.evaluate(X_test, y_test, verbose=0)
  
      return {'score': score, 'accuracy': accuracy}