To determine the average amount the trucking company should budget for fuel per gallon across its operations, we need to calculate the weighted average cost based on the probabilities and the fuel costs for each region.
Let's break down the steps:
1. Identify the given data:
- Southeast: Probability = 20% (0.20), Fuel Cost = \[tex]$3.10
- Southwest: Probability = 30% (0.30), Fuel Cost = \$[/tex]3.50
- California: Probability = 50% (0.50), Fuel Cost = \[tex]$4.05
2. Calculate the weighted cost for each region:
- For the Southeast:
\[
\text{Weighted Cost (Southeast)} = \text{Probability (Southeast)} \times \text{Fuel Cost (Southeast)}
\]
\[
= 0.20 \times 3.10 = 0.62
\]
- For the Southwest:
\[
\text{Weighted Cost (Southwest)} = \text{Probability (Southwest)} \times \text{Fuel Cost (Southwest)}
\]
\[
= 0.30 \times 3.50 = 1.05
\]
- For California:
\[
\text{Weighted Cost (California)} = \text{Probability (California)} \times \text{Fuel Cost (California)}
\]
\[
= 0.50 \times 4.05 = 2.025
\]
3. Sum the weighted costs to find the average cost:
\[
\text{Average Fuel Cost} = \text{Weighted Cost (Southeast)} + \text{Weighted Cost (Southwest)} + \text{Weighted Cost (California)}
\]
\[
= 0.62 + 1.05 + 2.025 = 3.695
\]
4. Round the average fuel cost to the nearest cent:
\[
\text{Average Fuel Cost (Rounded)} = 3.70
\]
Therefore, the company should budget \$[/tex]3.70 on average per gallon of fuel across its operations. The closest answer choice is [tex]\(\$ 3.70\)[/tex].
