Question

Sharpe Knife Company expects sales next year to be \(1,550,000 if the economy is strong, \)825,000 if the economy is steady, and $550,000 if the economy is weak. Mr. Sharpe believes there is a 30 percent probability the economy will be strong, a 40 percent probability of a steady economy, and a 30 percent probability of a weak economy. What is the expected level of sales for the next year?

Short answer

The expected level of sales for next year is $960,000.

Step-by-step solution

Information given in the question

The following information is provided:

Expected sales when the economy is strong = $1,550,000

Expected sales when the economy is steady = $825,000

Expected sales when the economy is weak = $550,000

Probability of strong economy = 30%

Probability of steady economy = 40%

Probability of weak economy = 30%

Expected sales for next year

The expected level ofsales for next year is $960,000.

$$\begin{gathered} \mathbf{Expected}\mathbf{}\mathbf{sales}\mathbf{}\mathbf{for}\mathbf{}\mathbf{next}\mathbf{}\mathbf{year}\mathbf{=}\mathbf{\sum }\mathbf{(}\mathbf{Expected}\mathbf{sales}\mathbf{\times }\mathbf{}\mathbf{Probability}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{30}\mathbf{\%}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{40}\mathbf{\%}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{550}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{30}\mathbf{\%}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{465}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{330}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{165}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{96}\mathbf{,}\mathbf{000} \end{gathered}$$