Calculate Batch Prediction Health Metrics

In production ML systems, monitoring the health of batch prediction jobs is essential for maintaining service reliability. Given a list of prediction results from a batch job, compute key health metrics that are commonly tracked in MLOps dashboards.

Each prediction result is a dictionary with:

• 'status': Either 'success' or 'error'
• 'confidence': A float between 0 and 1 (only present when status is 'success')

Write a function calculate_batch_health(predictions, confidence_threshold) that computes:

1. Success Rate: Percentage of predictions that completed successfully
2. Average Confidence: Mean confidence score of successful predictions (as a percentage)
3. Low Confidence Rate: Percentage of successful predictions with confidence below the threshold

The function should return a dictionary with these three metrics. If the input list is empty, return an empty dictionary. If there are no successful predictions, return success_rate as calculated and both confidence metrics as 0.0.

All returned values should be rounded to 2 decimal places.

def calculate_batch_health(predictions: list, confidence_threshold: float = 0.5) -> dict:
    """
    Calculate health metrics for a batch prediction job.
    
    Args:
        predictions: list of prediction results, each a dict with 'status' and optionally 'confidence'
        confidence_threshold: threshold below which a prediction is considered low confidence
    
    Returns:
        dict with keys: 'success_rate', 'avg_confidence', 'low_confidence_rate'
        All values as percentages (0-100), rounded to 2 decimal places.
    """
    pass