To determine the expected value of the total sales projection for Bronco Truck Parts, we can follow these steps:
1. Calculate the total sales for each outcome.
- For Outcome A:
- Units sold = 470
- Price per unit = \[tex]$23
- Total sales for Outcome A = \( 470 \times 23 = \$[/tex]10,810 \)
- For Outcome B:
- Units sold = 840
- Price per unit = \[tex]$31
- Total sales for Outcome B = \( 840 \times 31 = \$[/tex]26,040 \)
- For Outcome C:
- Units sold = 1,170
- Price per unit = \[tex]$36
- Total sales for Outcome C = \( 1,170 \times 36 = \$[/tex]42,120 \)
2. Determine the probability of each outcome.
- Probability of Outcome A = 0.40
- Probability of Outcome B = 0.40
- Probability of Outcome C = 0.20
3. Calculate the expected value of total sales.
The expected value of total sales is calculated by multiplying the total sales for each outcome by its respective probability and then summing these values:
[tex]\[
\text{Expected Value} = (\text{Probability of Outcome A} \times \text{Total Sales of Outcome A}) + (\text{Probability of Outcome B} \times \text{Total Sales of Outcome B}) + (\text{Probability of Outcome C} \times \text{Total Sales of Outcome C})
\][/tex]
Substituting the values we have:
[tex]\[
\text{Expected Value} = (0.40 \times 10,810) + (0.40 \times 26,040) + (0.20 \times 42,120)
\][/tex]
Simplifying further:
[tex]\[
\text{Expected Value} = 4,324 + 10,416 + 8,424 = \$23,164
\][/tex]
Therefore, the expected value of the total sales projection is \$23,164.
