At OHB bank the average employee salary is 40000 per year wi

At OHB bank, the average employee salary is $40,000 per year with a variance of 4,000,000. The CEO decides to award bonuses in the following way:
-A New Year

Solution

Answer: $300

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Note: The following notation varies from book-to-book.

mean = E(X) = $40,000

variance = V(X) = 4,000,000
--> standard deviation = SD(X) = sqrt(V(X)) = sqrt(4,000,000) = $2,000

a + bX = $600 + .15X
--> a = $600
--> b = .15

E(a + bX)
= a + bE(X)
= $600 + .15($40,000)
= $6,600

--> mean of the bonuses = $6,600

SD(a + bX)
= bSD(X)
= .15($2,000)
= $300

--> SD of the bonuses = $300

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I hope this helps! If you have any questions, please post them in my comment section. :)