Explanation:
To compute the mean compensation, we apply the following linear transformation to sales:
Y = α + βx
Y = 30,000 + 0.05x
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)
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
E(Y) = `$30`,000 + 0.05(`$300`,000) = `$45`,000
The correct answer is B because the mean compensation equals the base salary plus the expected bonus amount based on average sales.
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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