Problem

In a certain city, projections for the next year indicate there is a $20 \%$ chance that electronics jobs will increase by 1000 , a $50 \%$ chance that they will increase by 500 , and a $30 \%$. chance they will decrease by 900 . Find the expected change in the number of electronics jobs in that city in the next year. The expected change is an increase of jobs.

Solution

Step 1 :In a certain city, projections for the next year indicate there is a 20% chance that electronics jobs will increase by 1000, a 50% chance that they will increase by 500, and a 30% chance they will decrease by 900. We are asked to find the expected change in the number of electronics jobs in that city in the next year.

Step 2 :The expected change in the number of jobs can be calculated by multiplying each possible change in the number of jobs by the probability of that change occurring, and then summing these products. This is essentially calculating the weighted average of the possible changes in the number of jobs, where the weights are the probabilities of each change occurring.

Step 3 :Let's calculate the expected change: \(0.20 * 1000 + 0.50 * 500 - 0.30 * 900\)

Step 4 :After calculating the above expression, we find that the expected change is 180.0

Step 5 :So, the expected change in the number of electronics jobs in that city in the next year is an increase of \(\boxed{180}\).

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Source: https://solvelyapp.com/problems/Xogm5Rvxns/

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