a trucking company operates in three regions of the country. the table below depicts the probability that…

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

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

Answer

Explanation:

Step1: Convert probabilities to decimals

$20% = 0.2$, $30%=0.3$, $50% = 0.5$

Step2: Calculate weighted - average

The formula for the weighted - average is $\sum_{i = 1}^{n}p_{i}x_{i}$, where $p_{i}$ is the probability and $x_{i}$ is the value. [ \begin{align*} &0.2\times3.10+0.3\times3.50 + 0.5\times4.05\ =&0.62+1.05 + 2.025\ =&3.695 \end{align*} ]

Step3: Round the result

Rounding $3.695$ to the nearest cent gives $3.70$.

Answer:

$3.70$