Question

a trucking company operates in three regions of the country. the table below depicts the probability that each company truck is in the region and the fuel prices per gallon. what amount should the company budget on average for a gallon of fuel across its operations? round your answer to the nearest cent.
probability and fuel cost by region
region | probability in region | fuel cost per gallon
southeast | 20% | $3.10
southwest | 30% | $3.50
california | 50% | $4.05

○ $3.53
○ $3.55
○ $3.68
○ $3.70

Explanation:

Step1: Convert probabilities to decimals

Southeast: \( 20\% = 0.2 \), Southwest: \( 30\% = 0.3 \), California: \( 50\% = 0.5 \)

Step2: Calculate weighted cost for each region

Southeast: \( 0.2 \times 3.10 = 0.62 \)
Southwest: \( 0.3 \times 3.50 = 1.05 \)
California: \( 0.5 \times 4.05 = 2.025 \)

Step3: Sum weighted costs

Total average cost: \( 0.62 + 1.05 + 2.025 = 3.695 \approx 3.70 \)? Wait, no, wait: Wait, 0.62 + 1.05 is 1.67, plus 2.025 is 3.695, which rounds to $3.70? Wait, but let's check again. Wait, 3.10*0.2=0.62, 3.50*0.3=1.05, 4.05*0.5=2.025. Sum: 0.62 + 1.05 = 1.67; 1.67 + 2.025 = 3.695. Rounded to nearest cent is $3.70? Wait, but the options are $3.53, $3.55, $3.68, $3.70. Wait, maybe I miscalculated. Wait, 4.050.5: 40.5=2, 0.050.5=0.025, so 2.025. 3.500.3: 30.3=0.9, 0.500.3=0.15, so 1.05. 3.10*0.2=0.62. Sum: 0.62 + 1.05 = 1.67; 1.67 + 2.025 = 3.695, which is $3.70 when rounded to nearest cent. So the correct answer should be $3.70.

Answer:

\$3.70 (corresponding to the option with \$3.70)