Question

The Alliance Corp. expects to sell the following number of units of copper cables at the prices indicated, under three different scenarios in the economy. The probability of each outcome is indicated.

Outcome Probability Units Price
A 0.40 300 $35
B 0.40 520 50
C 0.20 810 60

What is the expected value of the total sales projection?

Answer 1

Explanation:

To calculate the expected value of the total sales projection, you multiply each outcome's total sales (units * price) by its probability and then sum up these values. The formula is:

\[ E(X) = \sum_{i} (x_i \cdot P_i) \]

where \(x_i\) is the value of the total sales for outcome \(i\) and \(P_i\) is the probability of outcome \(i\).

For this problem:

\[ E(X) = (300 \cdot 35 \cdot 0.40) + (520 \cdot 50 \cdot 0.40) + (810 \cdot 60 \cdot 0.20) \]

\[ E(X) = 4200 + 10400 + 9720 \]

\[ E(X) = 24320 \]

Therefore, the expected value of the total sales projection is $24,320.