Question

Customers at a fast-food restaurant buy both sandwiches and drinks. The mean number of sandwiches is 1.5 with a standard deviation of 0.5. The mean number of drinks is 1.45 with a standard deviation of 0.3. The correlation between the number of sandwiches and drinks purchased by the customer is 0.6. If the profit earned from selling a sandwich is $1.50 and from a drink is $1, what is the expected value and standard deviation of profit made from each customer.

Answer 1

X₁ : Number of sandwiches a customer buys

X₂ : Number of drinks a customer buys

Mean number of sandwiches : E(X₁) = 1.5

Standard deviation of X₁: = 0.5

Mean number of drinks : E(X₂) = 1.45

Standard deviation of X₂: = 0.3

correlation between the number of sandwiches and drinks purchased by the customer is 0.6

Profit earned from selling a sandwich = $1.50

Profit earned from selling a drink = $1

Profit from a customer Y = 1.50X₁+1X₂

Expected value of profit made from each customer = E(Y) = 1.50E(X₁)+E(X₂) = 1.5 x 1.5 + 1 x 1.45 = 2.25+1.45 = 3.7

Expected value of profit made from each customer = $3.7

Standard deviation of profit made from each customer:

Standard deviation of profit made from each customer = 0.960468636

Expected value of profit made from each customer = $3.7

Standard deviation of profit made from each customer = $0.960468636