Question

a farmer estimates her hens will produce 3,000 dozen more eggs this year than last year. she estimates the probability of her net profit or loss on each dozen eggs based on her costs. what is her expected profit on the total egg production?
her expected profit is $ square $. (simplify your answer.)
egg production last year. 12,000 dozen
estimated net profit per dozen eggs

Explanation:

Step1: Calculate the expected profit per dozen eggs

The formula for expected value \(E(X)=\sum_{i = 1}^{n}x_ip_i\), where \(x_i\) is the profit per dozen and \(p_i\) is the probability.

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Step2: Calculate the total expected profit

The total number of dozen eggs is \(12000 + 3000=15000\).
The total expected profit \(=E(X)\times15000\)
Since \(E(X)=2.6\), the total expected profit \(=2.6\times15000\)

Answer:

\(39000\)