Question

the federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the cars it makes. suppose that the models and mpg’s for a manufacturer are corsair (10 mpg), futura (12 mpg), retro (15 mpg), and envy (21 mpg). twenty percent of the cars sold are corsairs, 30% are futuras, 40% are retros, and 10% are envys. find the average mpg for this manufacturer. options: a. 15 mpg, b. 14 mpg, c. 10 mpg, d. 13.7 mpg

Explanation:

Step1: Identify each model's mpg and percentage

Corsair: 10 mpg, 20% = 0.2
Futura: 12 mpg, 30% = 0.3
Retro: 15 mpg, 40% = 0.4
Envy: 21 mpg, 10% = 0.1

Step2: Calculate weighted sum

Multiply each mpg by its percentage and sum:
\( (10 \times 0.2) + (12 \times 0.3) + (15 \times 0.4) + (21 \times 0.1) \)

Step3: Compute each term

\( 10 \times 0.2 = 2 \)
\( 12 \times 0.3 = 3.6 \)
\( 15 \times 0.4 = 6 \)
\( 21 \times 0.1 = 2.1 \)

Step4: Sum the results

\( 2 + 3.6 + 6 + 2.1 = 13.7 \)

Answer:

D. 13.7 mpg