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Answer: $45,000
To compute the mean compensation, we apply the following linear transformation to sales: ``` Y = α + βx Y = 30,000 + 0.05x ``` where Y is the transformed variable (mean compensation), X is the sales variable, β is the scale constant ($0.05/$1), and α is the shift constant. The mean compensation, i.e., mean of Y, is given by: ``` E(Y) = E(α + βx) = α + βE(X) ``` We know that average sales, E(X) = $300,000. Thus, ``` E(Y) = $30,000 + 0.05($300,000) = $45,000 ``` This calculation shows that the mean compensation is $45,000, which corresponds to option B.
Author: Nikitesh Somanthe
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At Capital Bank, the average salary among sales employees is $30,000 per year, and they are also entitled to a bonus of $0.05 for every dollar of sales brought in. Average sales amount to $300,000 per year. Determine the mean compensation received by employees.
A
$165,000
B
$45,000
C
$22,500
D
$330,000