Question

1. 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.
SEE EXAMPLE 1
Egg production last year: 12,000 dozen
Estimated Net Profit per Dozen Eggs
Net profit 8 6 4 2 °
8 6 4 2 0
(¢ per doz)
Probability 0.1 0.4 0.2 0.1 0.1 0.1

What is her expected profit per dozen eggs?

What is her expected profit on the total egg
production?
​

Answer 1

Expected profit per dozen eggs = 4 ¢

Expected profit on the total egg production = 60,000 ¢

Explanation:

Complete table as obtained online

Net Profit | 8 | 6 | 4 | 2 | 0 | -2

Probability |0.1|0.4|0.2|0.1|0.1|0.1

a) Expected profit per dozen eggs

Expected value is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

E(X) = (8×0.1) + (6×0.4) + (4×0.2) + (2×0.1) + (0×0.1) + (-2×0.1) = 4 ¢ per dozen

b) Expected profit on the total egg production

Last year, she had 12,000 dozen eggs

This year, she estimates 3,000 dozen more eggs

Estimated Total egg production this year = 12000 + 3000 = 15,000 dozen eggs

Expected profit per dozen eggs = 4 ¢

Expected profit on 15,000 dozen eggs = 15000 × 4 = 60,000 ¢

Hope this Helps!!!!