At a restaurant that sells appetizers: • 8% of the appetizers cost $1 each, • 20% of the appetizers cost $3 each, • 32% of the appetizers cost $5 each, • 40% of the appetizers cost $10 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.

Question

Katherine Little

Mathematics

22 March, 16:21

At a restaurant that sells appetizers: • 8% of the appetizers cost $1 each, • 20% of the appetizers cost $3 each, • 32% of the appetizers cost $5 each, • 40% of the appetizers cost $10 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.

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Bria Chan · Answer 1

12.0 (3 sf)

Step-by-step explanation:

E (X) = 0.08 (1) + 0.2 (3) + 0.32 (5) + 0.4 (10)

E (X) = 6.28

E (X²) =.08 (1²) +.2 (3²) +.32 (5²) +.4 (10²)

E (X²) = 49.88

Var (X) = E (X²) - [E (X) ]²

= 49.88 - 6.28² = 10.4416

Var (1.07X) = 1.07² Var (X)

= 1.1449*10.4416 = 11.95458784

12.0 (3 sf)