At a restaurant that sells appetizers: 8% of the appetizers cost $1 each, 20% of

Question:

At a restaurant that sells appetizers:
• 8% of the appetizers cost $1 each,
• 20% of the appetizers cost $2 each,
• 32% of the appetizers cost $3 each,
• 40% of the appetizers cost $4 each.
An appetizer is chosen at random, and X is its price. Each appetizer has 7% sales tax. So Y - 1.07X is the amount paid on the bill (in dollars). Find the variance of Y.